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$begingroup$
ALL ANIMALS ARE EQUAL
BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS
— from
Animal Farm
by George Orwell
A contrived simple
equivalence
rule applies neatly to numbers 0 through 99
but not to any other numbers.
Equivalences of numbers 0 through 19 are listed below,
accounting for almost all other eligible numbers as well,
where ‘=’ means “is equivalent to.”
(Each number is
reflexively
equivalent to itself.)
0 = no others
10 = no others
1 = no others
11 = 29 = 31 = 49 = 51 = 69 = 71 = 89 = 91
2 = no others
12 = 28 = 32 = 48 = 52 = 68 = 72 = 88 = 92
3 = no others
13 = 27 = 33 = 47 = 53 = 67 = 73 = 87 = 93
4 = no others
14 = 26 = 34 = 46 = 54 = 66 = 74 = 86 = 94
5 = no others
15 = 25 = 35 = 45 = 55 = 65 = 75 = 85 = 95
6 = no others
16 = 24 = 36 = 44 = 56 = 64 = 76 = 84 = 96
7 = no others
17 = 23 = 37 = 43 = 57 = 63 = 77 = 83 = 97
8 = no others
18 = 22 = 38 = 42 = 58 = 62 = 78 = 82 = 98
9 = no others
19 = 21 = 39 = 41 = 59 = 61 = 79 = 81 = 99
What would be the entry for 20 in this list?
20 = ___ . . . ?
Please use and explain the simplest possible rule,
not purely mathematical,
that accounts for every equivalence from 0 to 99.
lateral-thinking language
asked Mar 24 at 18:07
humnhumn
14.9k442133
$endgroup$
add a comment |
$begingroup$
ALL ANIMALS ARE EQUAL
BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS
— from
Animal Farm
by George Orwell
A contrived simple
equivalence
rule applies neatly to numbers 0 through 99
but not to any other numbers.
Equivalences of numbers 0 through 19 are listed below,
accounting for almost all other eligible numbers as well,
where ‘=’ means “is equivalent to.”
(Each number is
reflexively
equivalent to itself.)
0 = no others
10 = no others
1 = no others
11 = 29 = 31 = 49 = 51 = 69 = 71 = 89 = 91
2 = no others
12 = 28 = 32 = 48 = 52 = 68 = 72 = 88 = 92
3 = no others
13 = 27 = 33 = 47 = 53 = 67 = 73 = 87 = 93
4 = no others
14 = 26 = 34 = 46 = 54 = 66 = 74 = 86 = 94
5 = no others
15 = 25 = 35 = 45 = 55 = 65 = 75 = 85 = 95
6 = no others
16 = 24 = 36 = 44 = 56 = 64 = 76 = 84 = 96
7 = no others
17 = 23 = 37 = 43 = 57 = 63 = 77 = 83 = 97
8 = no others
18 = 22 = 38 = 42 = 58 = 62 = 78 = 82 = 98
9 = no others
19 = 21 = 39 = 41 = 59 = 61 = 79 = 81 = 99
What would be the entry for 20 in this list?
20 = ___ . . . ?
Please use and explain the simplest possible rule,
not purely mathematical,
that accounts for every equivalence from 0 to 99.
lateral-thinking language
asked Mar 24 at 18:07
humnhumn
14.9k442133
$endgroup$
2
$begingroup$
Apology for the lack of more specific tags: They would give away the solution.
$endgroup$
– humn
Mar 24 at 18:08
6
$begingroup$
Hurray, a humn puzzle! It's been a while.
$endgroup$
– Rand al'Thor
Mar 24 at 19:06
1
$begingroup$
Is there a way to "watch" a question so that I'm notified of new or accepted answers? I've already starred it.
$endgroup$
– MooseBoys
Mar 27 at 1:04
1
$begingroup$
To be clear, is the relation really only meaningful for numbers 0 thru 99, or are you just saying all numbers outside that range would be "no others"?
$endgroup$
– MooseBoys
Mar 27 at 1:07
$begingroup$
Thank you, @MooseBoys. Yes the relation only has relevance to numbers 0 through 99. "No others" would indeed be a great catch-all for other numbers.
$endgroup$
– humn
Mar 27 at 12:17
add a comment |
$begingroup$
ALL ANIMALS ARE EQUAL
BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS
— from
Animal Farm
by George Orwell
A contrived simple
equivalence
rule applies neatly to numbers 0 through 99
but not to any other numbers.
Equivalences of numbers 0 through 19 are listed below,
accounting for almost all other eligible numbers as well,
where ‘=’ means “is equivalent to.”
(Each number is
reflexively
equivalent to itself.)
0 = no others
10 = no others
1 = no others
11 = 29 = 31 = 49 = 51 = 69 = 71 = 89 = 91
2 = no others
12 = 28 = 32 = 48 = 52 = 68 = 72 = 88 = 92
3 = no others
13 = 27 = 33 = 47 = 53 = 67 = 73 = 87 = 93
4 = no others
14 = 26 = 34 = 46 = 54 = 66 = 74 = 86 = 94
5 = no others
15 = 25 = 35 = 45 = 55 = 65 = 75 = 85 = 95
6 = no others
16 = 24 = 36 = 44 = 56 = 64 = 76 = 84 = 96
7 = no others
17 = 23 = 37 = 43 = 57 = 63 = 77 = 83 = 97
8 = no others
18 = 22 = 38 = 42 = 58 = 62 = 78 = 82 = 98
9 = no others
19 = 21 = 39 = 41 = 59 = 61 = 79 = 81 = 99
What would be the entry for 20 in this list?
20 = ___ . . . ?
Please use and explain the simplest possible rule,
not purely mathematical,
that accounts for every equivalence from 0 to 99.
lateral-thinking language
asked Mar 24 at 18:07
humnhumn
14.9k442133
$endgroup$
ALL ANIMALS ARE EQUAL
BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS
— from
Animal Farm
by George Orwell
A contrived simple
equivalence
rule applies neatly to numbers 0 through 99
but not to any other numbers.
Equivalences of numbers 0 through 19 are listed below,
accounting for almost all other eligible numbers as well,
where ‘=’ means “is equivalent to.”
(Each number is
reflexively
equivalent to itself.)
0 = no others
10 = no others
1 = no others
11 = 29 = 31 = 49 = 51 = 69 = 71 = 89 = 91
2 = no others
12 = 28 = 32 = 48 = 52 = 68 = 72 = 88 = 92
3 = no others
13 = 27 = 33 = 47 = 53 = 67 = 73 = 87 = 93
4 = no others
14 = 26 = 34 = 46 = 54 = 66 = 74 = 86 = 94
5 = no others
15 = 25 = 35 = 45 = 55 = 65 = 75 = 85 = 95
6 = no others
16 = 24 = 36 = 44 = 56 = 64 = 76 = 84 = 96
7 = no others
17 = 23 = 37 = 43 = 57 = 63 = 77 = 83 = 97
8 = no others
18 = 22 = 38 = 42 = 58 = 62 = 78 = 82 = 98
9 = no others
19 = 21 = 39 = 41 = 59 = 61 = 79 = 81 = 99
What would be the entry for 20 in this list?
20 = ___ . . . ?
Please use and explain the simplest possible rule,
not purely mathematical,
that accounts for every equivalence from 0 to 99.
lateral-thinking language
lateral-thinking language
asked Mar 24 at 18:07
humnhumn
14.9k442133
asked Mar 24 at 18:07
humnhumn
14.9k442133
edited Apr 7 at 3:05
humn
asked Mar 24 at 18:07
humnhumn
14.9k442133
asked Mar 24 at 18:07
humnhumn
14.9k442133
asked Mar 24 at 18:07
humnhumn
14.9k442133
14.9k442133
2
$begingroup$
Apology for the lack of more specific tags: They would give away the solution.
$endgroup$
– humn
Mar 24 at 18:08
6
$begingroup$
Hurray, a humn puzzle! It's been a while.
$endgroup$
– Rand al'Thor
Mar 24 at 19:06
1
$begingroup$
Is there a way to "watch" a question so that I'm notified of new or accepted answers? I've already starred it.
$endgroup$
– MooseBoys
Mar 27 at 1:04
1
$begingroup$
To be clear, is the relation really only meaningful for numbers 0 thru 99, or are you just saying all numbers outside that range would be "no others"?
$endgroup$
– MooseBoys
Mar 27 at 1:07
$begingroup$
Thank you, @MooseBoys. Yes the relation only has relevance to numbers 0 through 99. "No others" would indeed be a great catch-all for other numbers.
$endgroup$
– humn
Mar 27 at 12:17
add a comment |
2
$begingroup$
Apology for the lack of more specific tags: They would give away the solution.
$endgroup$
– humn
Mar 24 at 18:08
6
$begingroup$
Hurray, a humn puzzle! It's been a while.
$endgroup$
– Rand al'Thor
Mar 24 at 19:06
1
$begingroup$
Is there a way to "watch" a question so that I'm notified of new or accepted answers? I've already starred it.
$endgroup$
– MooseBoys
Mar 27 at 1:04
1
$begingroup$
To be clear, is the relation really only meaningful for numbers 0 thru 99, or are you just saying all numbers outside that range would be "no others"?
$endgroup$
– MooseBoys
Mar 27 at 1:07
$begingroup$
Thank you, @MooseBoys. Yes the relation only has relevance to numbers 0 through 99. "No others" would indeed be a great catch-all for other numbers.
$endgroup$
– humn
Mar 27 at 12:17
2
2
$begingroup$
Apology for the lack of more specific tags: They would give away the solution.
$endgroup$
– humn
Mar 24 at 18:08
$begingroup$
Apology for the lack of more specific tags: They would give away the solution.
$endgroup$
– humn
Mar 24 at 18:08
6
6
$begingroup$
Hurray, a humn puzzle! It's been a while.
$endgroup$
– Rand al'Thor
Mar 24 at 19:06
$begingroup$
Hurray, a humn puzzle! It's been a while.
$endgroup$
– Rand al'Thor
Mar 24 at 19:06
1
1
$begingroup$
Is there a way to "watch" a question so that I'm notified of new or accepted answers? I've already starred it.
$endgroup$
– MooseBoys
Mar 27 at 1:04
$begingroup$
Is there a way to "watch" a question so that I'm notified of new or accepted answers? I've already starred it.
$endgroup$
– MooseBoys
Mar 27 at 1:04
1
1
$begingroup$
To be clear, is the relation really only meaningful for numbers 0 thru 99, or are you just saying all numbers outside that range would be "no others"?
$endgroup$
– MooseBoys
Mar 27 at 1:07
$begingroup$
To be clear, is the relation really only meaningful for numbers 0 thru 99, or are you just saying all numbers outside that range would be "no others"?
$endgroup$
– MooseBoys
Mar 27 at 1:07
$begingroup$
Thank you, @MooseBoys. Yes the relation only has relevance to numbers 0 through 99. "No others" would indeed be a great catch-all for other numbers.
$endgroup$
– humn
Mar 27 at 12:17
$begingroup$
Thank you, @MooseBoys. Yes the relation only has relevance to numbers 0 through 99. "No others" would indeed be a great catch-all for other numbers.
$endgroup$
– humn
Mar 27 at 12:17
add a comment |
5 Answers
5
active
oldest
votes
$begingroup$
Answer:
20 = no others
Reason: (humn has told me that this is wrong but it's my favorite guess of mine)
Because you gave us a list of equivalences which are more equal than others. So we can assume the remaining numbers are less equal and therefore only equal to themselves.
Other guesses:
Xilpex's rule applies if no digits are zero. If any digit is zero (
2can be written as02) then there are no equivalents
Because the rules are contrived so I can simply invent whatever I want for the rules that aren't given to me.
answered Mar 24 at 23:29
ferretferret
2,0251828
$endgroup$
$begingroup$
Correct answer, @ferret! But the reasoning is more complicated than necessary.
$endgroup$
– humn
Mar 25 at 2:02
1
$begingroup$
@humn edited with a new "lateral thinking" attempt
$endgroup$
– ferret
Mar 25 at 3:04
1
$begingroup$
You're on the way, @ferret, and gave me an idea for another puzzle. Still missing the essential ingredient.
$endgroup$
– humn
Mar 25 at 4:06
1
$begingroup$
@humn is it because they are rot13 pbagevirq?
$endgroup$
– ferret
Mar 25 at 5:31
1
$begingroup$
Thank you for playing along, @ferret. Pleasure to have met you.
$endgroup$
– humn
Mar 25 at 17:06
|
show 4 more comments
$begingroup$
20 = no others. same as 0 to 10. because it breaks the following pattern. The green cells are the numbers given and the colored cells is the sum their digits above them. Numbers 0 - 10 break the pattern of the sums as well. Hence the "no others" as they don't follow the pattern of the sums as others
i know there is no 100, 101, i used excel for this, regardless it still doesn't follow the pattern of the sums either way
answered Apr 4 at 21:52
MelMel
4418
$endgroup$
$begingroup$
Congratulations on the correct answer. And what a wonderfully visual and consistent explanation. Yet the intended explanation is simpler and not nearly as gorgeous.
$endgroup$
– humn
Apr 7 at 3:21
$begingroup$
@humn well, the non mathematical explanation would be that numbers with leading or trailing zeroes have no equivalence. 00,01,02,03,04,05,06,07,08,09,10,20
$endgroup$
– Mel
Apr 7 at 9:38
$begingroup$
Your non mathematical 0s approach does fit the pattern, @Mel, but doesn't explain the equivalences as well as your excel solution.
$endgroup$
– humn
Apr 7 at 11:33
add a comment |
$begingroup$
My first thought was
The equivalence classes are based on the distance of a number to the closest multiple of 20:
$$|11 - 20| = 9, quad |29 - 20| = 9,quad |31 - 40| = 9,quad ldots$$
However, that did not explain 0 through 10. I could add a 'except for 1 through 10' to my rule, but that wasn't very satisfying.
The second thing I came up with was:
For a number $n$ made of two digits $a$ and $b$, we have $n = acdot 10 + b$. If we say those are equivalent to $m=acdot 10 - b$, they are recursively equivalent to a lot of numbers. For example, $$97 = 9cdot 10 + 7$$ $$9cdot 10 - 7 = 83 = 8cdot 10 + 3$$ $$8cdot10 - 3 = 77 = 7cdot 10 + 7$$ And so on: $97 rightarrow 83 rightarrow 77 rightarrow 63 rightarrow 57 rightarrow 43 rightarrow 37 rightarrow ldots$. This shows that numbers with a zero as second digit do not have any other equivalent numbers, as this process would not lead to any new numbers: $$20 = 2cdot 10 + 0$$ $$2cdot10 - 0 = 20$$ $20 rightarrow 20 rightarrow ldots$. The only way I managed to explain $1,ldots,9$ here is to explain you simply can't apply this process to those numbers, as they do not have two digits.
This doesn't work if you accept that 09 is a perfectly fine way of writing 9. So I'm still not very satisfied with this solution.
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
$endgroup$
$begingroup$
M-ou-se, the indended explanation is hidden inside your second approach (about multiples of 10). That is the closest any has yet gotten! Still, the intended solution is simpler and not quite as mathematical.
$endgroup$
– humn
Apr 7 at 11:42
add a comment |
$begingroup$
20 would be:
20 = 20 = 40 = 40 = 60 = 60 = 80 = 80 = 100
Explanation:
The rule (vertically) is: Line 1 + 1, then Line 2 - 1, and so on.
answered Mar 24 at 18:19
XilpexXilpex
302112
$endgroup$
3
$begingroup$
Thank you for taking the bait, Xilpex. Not quite the solution, though. For instance, it doesn't explain the entry for 10.
$endgroup$
– humn
Mar 24 at 18:23
1
$begingroup$
@humn Ok. I'll see if there is any other answer... :D
$endgroup$
– Xilpex
Mar 24 at 18:25
1
$begingroup$
Plus there is no $100$.
$endgroup$
– Arnaud Mortier
Mar 24 at 18:36
add a comment |
$begingroup$
0 = no others 10 = no others 20 = no others
1 = no others 1 1 = 2 9 = 3 1 = 4 9 = 5 1 = 69 = 71 = 89 = 91
2 = no others 1 2 = 2 8 = 3 2 = 4 8 = 5 2 = 68 = 72 = 88 = 92
3 = no others 1 3 = 2 7 = 3 3 = 4 7 = 5 3 = 67 = 73 = 87 = 93
4 = no others 1 4 = 2 6 = 3 4 = 4 6 = 5 4 = 66 = 74 = 86 = 94
5 = no others 1 5 = 2 5 = 3 5 = 4 5 = 5 5 = 65 = 75 = 85 = 95
6 = no others 1 6 = 2 4 = 3 6 = 4 4 = 5 6 = 64 = 76 = 84 = 96
7 = no others 1 7 = 2 3 = 3 7 = 4 3 = 5 7 = 63 = 77 = 83 = 97
8 = no others 1 8 = 2 2 = 3 8 = 4 2 = 5 8 = 62 = 78 = 82 = 98
9 = no others 1 9 = 2 1 = 3 9 = 4 1 = 5 9 = 61 = 79 = 81 = 99
Delete the tens digit, like follow:
0 = no others 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
1 = no others 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1
2 = no others 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2
3 = no others 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3
4 = no others 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4
5 = no others 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5
6 = no others 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6
7 = no others 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7
8 = no others 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8
9 = no others 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9
So there is no rules to 0,
20 = no others
answered Mar 25 at 6:10
user58107user58107
212
$endgroup$
1
$begingroup$
Keep going, @user58107! It's simpler than that.
$endgroup$
– humn
Mar 25 at 6:42
2
$begingroup$
look the column, my English very poor, can't explain clarification.
$endgroup$
– user58107
Mar 25 at 6:46
$begingroup$
Oh, oh oh oh, @user58107, this puzzle relies on English. (Big give-away.) Thank you for hitching the ride.
$endgroup$
– humn
Mar 25 at 6:52
1
$begingroup$
@humn Maybe a language tag then?
$endgroup$
– Rubio♦
Apr 6 at 4:07
$begingroup$
Right, @Rubio,languagetag added. I was trying to not give away that aspect but did in the comment above and the time is ripe anyway.
$endgroup$
– humn
Apr 7 at 3:11
add a comment |
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5 Answers
5
active
oldest
votes
5 Answers
5
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Answer:
20 = no others
Reason: (humn has told me that this is wrong but it's my favorite guess of mine)
Because you gave us a list of equivalences which are more equal than others. So we can assume the remaining numbers are less equal and therefore only equal to themselves.
Other guesses:
Xilpex's rule applies if no digits are zero. If any digit is zero (
2can be written as02) then there are no equivalents
Because the rules are contrived so I can simply invent whatever I want for the rules that aren't given to me.
answered Mar 24 at 23:29
ferretferret
2,0251828
$endgroup$
$begingroup$
Correct answer, @ferret! But the reasoning is more complicated than necessary.
$endgroup$
– humn
Mar 25 at 2:02
1
$begingroup$
@humn edited with a new "lateral thinking" attempt
$endgroup$
– ferret
Mar 25 at 3:04
1
$begingroup$
You're on the way, @ferret, and gave me an idea for another puzzle. Still missing the essential ingredient.
$endgroup$
– humn
Mar 25 at 4:06
1
$begingroup$
@humn is it because they are rot13 pbagevirq?
$endgroup$
– ferret
Mar 25 at 5:31
1
$begingroup$
Thank you for playing along, @ferret. Pleasure to have met you.
$endgroup$
– humn
Mar 25 at 17:06
|
show 4 more comments
$begingroup$
Answer:
20 = no others
Reason: (humn has told me that this is wrong but it's my favorite guess of mine)
Because you gave us a list of equivalences which are more equal than others. So we can assume the remaining numbers are less equal and therefore only equal to themselves.
Other guesses:
Xilpex's rule applies if no digits are zero. If any digit is zero (
2can be written as02) then there are no equivalents
Because the rules are contrived so I can simply invent whatever I want for the rules that aren't given to me.
answered Mar 24 at 23:29
ferretferret
2,0251828
$endgroup$
$begingroup$
Correct answer, @ferret! But the reasoning is more complicated than necessary.
$endgroup$
– humn
Mar 25 at 2:02
1
$begingroup$
@humn edited with a new "lateral thinking" attempt
$endgroup$
– ferret
Mar 25 at 3:04
1
$begingroup$
You're on the way, @ferret, and gave me an idea for another puzzle. Still missing the essential ingredient.
$endgroup$
– humn
Mar 25 at 4:06
1
$begingroup$
@humn is it because they are rot13 pbagevirq?
$endgroup$
– ferret
Mar 25 at 5:31
1
$begingroup$
Thank you for playing along, @ferret. Pleasure to have met you.
$endgroup$
– humn
Mar 25 at 17:06
|
show 4 more comments
$begingroup$
Answer:
20 = no others
Reason: (humn has told me that this is wrong but it's my favorite guess of mine)
Because you gave us a list of equivalences which are more equal than others. So we can assume the remaining numbers are less equal and therefore only equal to themselves.
Other guesses:
Xilpex's rule applies if no digits are zero. If any digit is zero (
2can be written as02) then there are no equivalents
Because the rules are contrived so I can simply invent whatever I want for the rules that aren't given to me.
answered Mar 24 at 23:29
ferretferret
2,0251828
$endgroup$
Answer:
20 = no others
Reason: (humn has told me that this is wrong but it's my favorite guess of mine)
Because you gave us a list of equivalences which are more equal than others. So we can assume the remaining numbers are less equal and therefore only equal to themselves.
Other guesses:
Xilpex's rule applies if no digits are zero. If any digit is zero (
2can be written as02) then there are no equivalents
Because the rules are contrived so I can simply invent whatever I want for the rules that aren't given to me.
answered Mar 24 at 23:29
ferretferret
2,0251828
edited Mar 25 at 17:07
answered Mar 24 at 23:29
ferretferret
2,0251828
answered Mar 24 at 23:29
ferretferret
2,0251828
answered Mar 24 at 23:29
ferretferret
2,0251828
2,0251828
$begingroup$
Correct answer, @ferret! But the reasoning is more complicated than necessary.
$endgroup$
– humn
Mar 25 at 2:02
1
$begingroup$
@humn edited with a new "lateral thinking" attempt
$endgroup$
– ferret
Mar 25 at 3:04
1
$begingroup$
You're on the way, @ferret, and gave me an idea for another puzzle. Still missing the essential ingredient.
$endgroup$
– humn
Mar 25 at 4:06
1
$begingroup$
@humn is it because they are rot13 pbagevirq?
$endgroup$
– ferret
Mar 25 at 5:31
1
$begingroup$
Thank you for playing along, @ferret. Pleasure to have met you.
$endgroup$
– humn
Mar 25 at 17:06
|
show 4 more comments
$begingroup$
Correct answer, @ferret! But the reasoning is more complicated than necessary.
$endgroup$
– humn
Mar 25 at 2:02
1
$begingroup$
@humn edited with a new "lateral thinking" attempt
$endgroup$
– ferret
Mar 25 at 3:04
1
$begingroup$
You're on the way, @ferret, and gave me an idea for another puzzle. Still missing the essential ingredient.
$endgroup$
– humn
Mar 25 at 4:06
1
$begingroup$
@humn is it because they are rot13 pbagevirq?
$endgroup$
– ferret
Mar 25 at 5:31
1
$begingroup$
Thank you for playing along, @ferret. Pleasure to have met you.
$endgroup$
– humn
Mar 25 at 17:06
$begingroup$
Correct answer, @ferret! But the reasoning is more complicated than necessary.
$endgroup$
– humn
Mar 25 at 2:02
$begingroup$
Correct answer, @ferret! But the reasoning is more complicated than necessary.
$endgroup$
– humn
Mar 25 at 2:02
1
1
$begingroup$
@humn edited with a new "lateral thinking" attempt
$endgroup$
– ferret
Mar 25 at 3:04
$begingroup$
@humn edited with a new "lateral thinking" attempt
$endgroup$
– ferret
Mar 25 at 3:04
1
1
$begingroup$
You're on the way, @ferret, and gave me an idea for another puzzle. Still missing the essential ingredient.
$endgroup$
– humn
Mar 25 at 4:06
$begingroup$
You're on the way, @ferret, and gave me an idea for another puzzle. Still missing the essential ingredient.
$endgroup$
– humn
Mar 25 at 4:06
1
1
$begingroup$
@humn is it because they are rot13 pbagevirq?
$endgroup$
– ferret
Mar 25 at 5:31
$begingroup$
@humn is it because they are rot13 pbagevirq?
$endgroup$
– ferret
Mar 25 at 5:31
1
1
$begingroup$
Thank you for playing along, @ferret. Pleasure to have met you.
$endgroup$
– humn
Mar 25 at 17:06
$begingroup$
Thank you for playing along, @ferret. Pleasure to have met you.
$endgroup$
– humn
Mar 25 at 17:06
|
show 4 more comments
$begingroup$
20 = no others. same as 0 to 10. because it breaks the following pattern. The green cells are the numbers given and the colored cells is the sum their digits above them. Numbers 0 - 10 break the pattern of the sums as well. Hence the "no others" as they don't follow the pattern of the sums as others
i know there is no 100, 101, i used excel for this, regardless it still doesn't follow the pattern of the sums either way
answered Apr 4 at 21:52
MelMel
4418
$endgroup$
$begingroup$
Congratulations on the correct answer. And what a wonderfully visual and consistent explanation. Yet the intended explanation is simpler and not nearly as gorgeous.
$endgroup$
– humn
Apr 7 at 3:21
$begingroup$
@humn well, the non mathematical explanation would be that numbers with leading or trailing zeroes have no equivalence. 00,01,02,03,04,05,06,07,08,09,10,20
$endgroup$
– Mel
Apr 7 at 9:38
$begingroup$
Your non mathematical 0s approach does fit the pattern, @Mel, but doesn't explain the equivalences as well as your excel solution.
$endgroup$
– humn
Apr 7 at 11:33
add a comment |
$begingroup$
20 = no others. same as 0 to 10. because it breaks the following pattern. The green cells are the numbers given and the colored cells is the sum their digits above them. Numbers 0 - 10 break the pattern of the sums as well. Hence the "no others" as they don't follow the pattern of the sums as others
i know there is no 100, 101, i used excel for this, regardless it still doesn't follow the pattern of the sums either way
answered Apr 4 at 21:52
MelMel
4418
$endgroup$
$begingroup$
Congratulations on the correct answer. And what a wonderfully visual and consistent explanation. Yet the intended explanation is simpler and not nearly as gorgeous.
$endgroup$
– humn
Apr 7 at 3:21
$begingroup$
@humn well, the non mathematical explanation would be that numbers with leading or trailing zeroes have no equivalence. 00,01,02,03,04,05,06,07,08,09,10,20
$endgroup$
– Mel
Apr 7 at 9:38
$begingroup$
Your non mathematical 0s approach does fit the pattern, @Mel, but doesn't explain the equivalences as well as your excel solution.
$endgroup$
– humn
Apr 7 at 11:33
add a comment |
$begingroup$
20 = no others. same as 0 to 10. because it breaks the following pattern. The green cells are the numbers given and the colored cells is the sum their digits above them. Numbers 0 - 10 break the pattern of the sums as well. Hence the "no others" as they don't follow the pattern of the sums as others
i know there is no 100, 101, i used excel for this, regardless it still doesn't follow the pattern of the sums either way
answered Apr 4 at 21:52
MelMel
4418
$endgroup$
20 = no others. same as 0 to 10. because it breaks the following pattern. The green cells are the numbers given and the colored cells is the sum their digits above them. Numbers 0 - 10 break the pattern of the sums as well. Hence the "no others" as they don't follow the pattern of the sums as others
i know there is no 100, 101, i used excel for this, regardless it still doesn't follow the pattern of the sums either way
answered Apr 4 at 21:52
MelMel
4418
edited Apr 4 at 22:03
answered Apr 4 at 21:52
MelMel
4418
answered Apr 4 at 21:52
MelMel
4418
answered Apr 4 at 21:52
MelMel
4418
4418
$begingroup$
Congratulations on the correct answer. And what a wonderfully visual and consistent explanation. Yet the intended explanation is simpler and not nearly as gorgeous.
$endgroup$
– humn
Apr 7 at 3:21
$begingroup$
@humn well, the non mathematical explanation would be that numbers with leading or trailing zeroes have no equivalence. 00,01,02,03,04,05,06,07,08,09,10,20
$endgroup$
– Mel
Apr 7 at 9:38
$begingroup$
Your non mathematical 0s approach does fit the pattern, @Mel, but doesn't explain the equivalences as well as your excel solution.
$endgroup$
– humn
Apr 7 at 11:33
add a comment |
$begingroup$
Congratulations on the correct answer. And what a wonderfully visual and consistent explanation. Yet the intended explanation is simpler and not nearly as gorgeous.
$endgroup$
– humn
Apr 7 at 3:21
$begingroup$
@humn well, the non mathematical explanation would be that numbers with leading or trailing zeroes have no equivalence. 00,01,02,03,04,05,06,07,08,09,10,20
$endgroup$
– Mel
Apr 7 at 9:38
$begingroup$
Your non mathematical 0s approach does fit the pattern, @Mel, but doesn't explain the equivalences as well as your excel solution.
$endgroup$
– humn
Apr 7 at 11:33
$begingroup$
Congratulations on the correct answer. And what a wonderfully visual and consistent explanation. Yet the intended explanation is simpler and not nearly as gorgeous.
$endgroup$
– humn
Apr 7 at 3:21
$begingroup$
Congratulations on the correct answer. And what a wonderfully visual and consistent explanation. Yet the intended explanation is simpler and not nearly as gorgeous.
$endgroup$
– humn
Apr 7 at 3:21
$begingroup$
@humn well, the non mathematical explanation would be that numbers with leading or trailing zeroes have no equivalence. 00,01,02,03,04,05,06,07,08,09,10,20
$endgroup$
– Mel
Apr 7 at 9:38
$begingroup$
@humn well, the non mathematical explanation would be that numbers with leading or trailing zeroes have no equivalence. 00,01,02,03,04,05,06,07,08,09,10,20
$endgroup$
– Mel
Apr 7 at 9:38
$begingroup$
Your non mathematical 0s approach does fit the pattern, @Mel, but doesn't explain the equivalences as well as your excel solution.
$endgroup$
– humn
Apr 7 at 11:33
$begingroup$
Your non mathematical 0s approach does fit the pattern, @Mel, but doesn't explain the equivalences as well as your excel solution.
$endgroup$
– humn
Apr 7 at 11:33
add a comment |
$begingroup$
My first thought was
The equivalence classes are based on the distance of a number to the closest multiple of 20:
$$|11 - 20| = 9, quad |29 - 20| = 9,quad |31 - 40| = 9,quad ldots$$
However, that did not explain 0 through 10. I could add a 'except for 1 through 10' to my rule, but that wasn't very satisfying.
The second thing I came up with was:
For a number $n$ made of two digits $a$ and $b$, we have $n = acdot 10 + b$. If we say those are equivalent to $m=acdot 10 - b$, they are recursively equivalent to a lot of numbers. For example, $$97 = 9cdot 10 + 7$$ $$9cdot 10 - 7 = 83 = 8cdot 10 + 3$$ $$8cdot10 - 3 = 77 = 7cdot 10 + 7$$ And so on: $97 rightarrow 83 rightarrow 77 rightarrow 63 rightarrow 57 rightarrow 43 rightarrow 37 rightarrow ldots$. This shows that numbers with a zero as second digit do not have any other equivalent numbers, as this process would not lead to any new numbers: $$20 = 2cdot 10 + 0$$ $$2cdot10 - 0 = 20$$ $20 rightarrow 20 rightarrow ldots$. The only way I managed to explain $1,ldots,9$ here is to explain you simply can't apply this process to those numbers, as they do not have two digits.
This doesn't work if you accept that 09 is a perfectly fine way of writing 9. So I'm still not very satisfied with this solution.
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
$endgroup$
$begingroup$
M-ou-se, the indended explanation is hidden inside your second approach (about multiples of 10). That is the closest any has yet gotten! Still, the intended solution is simpler and not quite as mathematical.
$endgroup$
– humn
Apr 7 at 11:42
add a comment |
$begingroup$
My first thought was
The equivalence classes are based on the distance of a number to the closest multiple of 20:
$$|11 - 20| = 9, quad |29 - 20| = 9,quad |31 - 40| = 9,quad ldots$$
However, that did not explain 0 through 10. I could add a 'except for 1 through 10' to my rule, but that wasn't very satisfying.
The second thing I came up with was:
For a number $n$ made of two digits $a$ and $b$, we have $n = acdot 10 + b$. If we say those are equivalent to $m=acdot 10 - b$, they are recursively equivalent to a lot of numbers. For example, $$97 = 9cdot 10 + 7$$ $$9cdot 10 - 7 = 83 = 8cdot 10 + 3$$ $$8cdot10 - 3 = 77 = 7cdot 10 + 7$$ And so on: $97 rightarrow 83 rightarrow 77 rightarrow 63 rightarrow 57 rightarrow 43 rightarrow 37 rightarrow ldots$. This shows that numbers with a zero as second digit do not have any other equivalent numbers, as this process would not lead to any new numbers: $$20 = 2cdot 10 + 0$$ $$2cdot10 - 0 = 20$$ $20 rightarrow 20 rightarrow ldots$. The only way I managed to explain $1,ldots,9$ here is to explain you simply can't apply this process to those numbers, as they do not have two digits.
This doesn't work if you accept that 09 is a perfectly fine way of writing 9. So I'm still not very satisfied with this solution.
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
$endgroup$
$begingroup$
M-ou-se, the indended explanation is hidden inside your second approach (about multiples of 10). That is the closest any has yet gotten! Still, the intended solution is simpler and not quite as mathematical.
$endgroup$
– humn
Apr 7 at 11:42
add a comment |
$begingroup$
My first thought was
The equivalence classes are based on the distance of a number to the closest multiple of 20:
$$|11 - 20| = 9, quad |29 - 20| = 9,quad |31 - 40| = 9,quad ldots$$
However, that did not explain 0 through 10. I could add a 'except for 1 through 10' to my rule, but that wasn't very satisfying.
The second thing I came up with was:
For a number $n$ made of two digits $a$ and $b$, we have $n = acdot 10 + b$. If we say those are equivalent to $m=acdot 10 - b$, they are recursively equivalent to a lot of numbers. For example, $$97 = 9cdot 10 + 7$$ $$9cdot 10 - 7 = 83 = 8cdot 10 + 3$$ $$8cdot10 - 3 = 77 = 7cdot 10 + 7$$ And so on: $97 rightarrow 83 rightarrow 77 rightarrow 63 rightarrow 57 rightarrow 43 rightarrow 37 rightarrow ldots$. This shows that numbers with a zero as second digit do not have any other equivalent numbers, as this process would not lead to any new numbers: $$20 = 2cdot 10 + 0$$ $$2cdot10 - 0 = 20$$ $20 rightarrow 20 rightarrow ldots$. The only way I managed to explain $1,ldots,9$ here is to explain you simply can't apply this process to those numbers, as they do not have two digits.
This doesn't work if you accept that 09 is a perfectly fine way of writing 9. So I'm still not very satisfied with this solution.
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
$endgroup$
My first thought was
The equivalence classes are based on the distance of a number to the closest multiple of 20:
$$|11 - 20| = 9, quad |29 - 20| = 9,quad |31 - 40| = 9,quad ldots$$
However, that did not explain 0 through 10. I could add a 'except for 1 through 10' to my rule, but that wasn't very satisfying.
The second thing I came up with was:
For a number $n$ made of two digits $a$ and $b$, we have $n = acdot 10 + b$. If we say those are equivalent to $m=acdot 10 - b$, they are recursively equivalent to a lot of numbers. For example, $$97 = 9cdot 10 + 7$$ $$9cdot 10 - 7 = 83 = 8cdot 10 + 3$$ $$8cdot10 - 3 = 77 = 7cdot 10 + 7$$ And so on: $97 rightarrow 83 rightarrow 77 rightarrow 63 rightarrow 57 rightarrow 43 rightarrow 37 rightarrow ldots$. This shows that numbers with a zero as second digit do not have any other equivalent numbers, as this process would not lead to any new numbers: $$20 = 2cdot 10 + 0$$ $$2cdot10 - 0 = 20$$ $20 rightarrow 20 rightarrow ldots$. The only way I managed to explain $1,ldots,9$ here is to explain you simply can't apply this process to those numbers, as they do not have two digits.
This doesn't work if you accept that 09 is a perfectly fine way of writing 9. So I'm still not very satisfied with this solution.
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
edited Apr 7 at 10:10
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
answered Apr 7 at 10:00
M-ou-seM-ou-se
1313
1313
$begingroup$
M-ou-se, the indended explanation is hidden inside your second approach (about multiples of 10). That is the closest any has yet gotten! Still, the intended solution is simpler and not quite as mathematical.
$endgroup$
– humn
Apr 7 at 11:42
add a comment |
$begingroup$
M-ou-se, the indended explanation is hidden inside your second approach (about multiples of 10). That is the closest any has yet gotten! Still, the intended solution is simpler and not quite as mathematical.
$endgroup$
– humn
Apr 7 at 11:42
$begingroup$
M-ou-se, the indended explanation is hidden inside your second approach (about multiples of 10). That is the closest any has yet gotten! Still, the intended solution is simpler and not quite as mathematical.
$endgroup$
– humn
Apr 7 at 11:42
$begingroup$
M-ou-se, the indended explanation is hidden inside your second approach (about multiples of 10). That is the closest any has yet gotten! Still, the intended solution is simpler and not quite as mathematical.
$endgroup$
– humn
Apr 7 at 11:42
add a comment |
$begingroup$
20 would be:
20 = 20 = 40 = 40 = 60 = 60 = 80 = 80 = 100
Explanation:
The rule (vertically) is: Line 1 + 1, then Line 2 - 1, and so on.
answered Mar 24 at 18:19
XilpexXilpex
302112
$endgroup$
3
$begingroup$
Thank you for taking the bait, Xilpex. Not quite the solution, though. For instance, it doesn't explain the entry for 10.
$endgroup$
– humn
Mar 24 at 18:23
1
$begingroup$
@humn Ok. I'll see if there is any other answer... :D
$endgroup$
– Xilpex
Mar 24 at 18:25
1
$begingroup$
Plus there is no $100$.
$endgroup$
– Arnaud Mortier
Mar 24 at 18:36
add a comment |
$begingroup$
20 would be:
20 = 20 = 40 = 40 = 60 = 60 = 80 = 80 = 100
Explanation:
The rule (vertically) is: Line 1 + 1, then Line 2 - 1, and so on.
answered Mar 24 at 18:19
XilpexXilpex
302112
$endgroup$
3
$begingroup$
Thank you for taking the bait, Xilpex. Not quite the solution, though. For instance, it doesn't explain the entry for 10.
$endgroup$
– humn
Mar 24 at 18:23
1
$begingroup$
@humn Ok. I'll see if there is any other answer... :D
$endgroup$
– Xilpex
Mar 24 at 18:25
1
$begingroup$
Plus there is no $100$.
$endgroup$
– Arnaud Mortier
Mar 24 at 18:36
add a comment |
$begingroup$
20 would be:
20 = 20 = 40 = 40 = 60 = 60 = 80 = 80 = 100
Explanation:
The rule (vertically) is: Line 1 + 1, then Line 2 - 1, and so on.
answered Mar 24 at 18:19
XilpexXilpex
302112
$endgroup$
20 would be:
20 = 20 = 40 = 40 = 60 = 60 = 80 = 80 = 100
Explanation:
The rule (vertically) is: Line 1 + 1, then Line 2 - 1, and so on.
answered Mar 24 at 18:19
XilpexXilpex
302112
answered Mar 24 at 18:19
XilpexXilpex
302112
answered Mar 24 at 18:19
XilpexXilpex
302112
answered Mar 24 at 18:19
XilpexXilpex
302112
302112
3
$begingroup$
Thank you for taking the bait, Xilpex. Not quite the solution, though. For instance, it doesn't explain the entry for 10.
$endgroup$
– humn
Mar 24 at 18:23
1
$begingroup$
@humn Ok. I'll see if there is any other answer... :D
$endgroup$
– Xilpex
Mar 24 at 18:25
1
$begingroup$
Plus there is no $100$.
$endgroup$
– Arnaud Mortier
Mar 24 at 18:36
add a comment |
3
$begingroup$
Thank you for taking the bait, Xilpex. Not quite the solution, though. For instance, it doesn't explain the entry for 10.
$endgroup$
– humn
Mar 24 at 18:23
1
$begingroup$
@humn Ok. I'll see if there is any other answer... :D
$endgroup$
– Xilpex
Mar 24 at 18:25
1
$begingroup$
Plus there is no $100$.
$endgroup$
– Arnaud Mortier
Mar 24 at 18:36
3
3
$begingroup$
Thank you for taking the bait, Xilpex. Not quite the solution, though. For instance, it doesn't explain the entry for 10.
$endgroup$
– humn
Mar 24 at 18:23
$begingroup$
Thank you for taking the bait, Xilpex. Not quite the solution, though. For instance, it doesn't explain the entry for 10.
$endgroup$
– humn
Mar 24 at 18:23
1
1
$begingroup$
@humn Ok. I'll see if there is any other answer... :D
$endgroup$
– Xilpex
Mar 24 at 18:25
$begingroup$
@humn Ok. I'll see if there is any other answer... :D
$endgroup$
– Xilpex
Mar 24 at 18:25
1
1
$begingroup$
Plus there is no $100$.
$endgroup$
– Arnaud Mortier
Mar 24 at 18:36
$begingroup$
Plus there is no $100$.
$endgroup$
– Arnaud Mortier
Mar 24 at 18:36
add a comment |
$begingroup$
0 = no others 10 = no others 20 = no others
1 = no others 1 1 = 2 9 = 3 1 = 4 9 = 5 1 = 69 = 71 = 89 = 91
2 = no others 1 2 = 2 8 = 3 2 = 4 8 = 5 2 = 68 = 72 = 88 = 92
3 = no others 1 3 = 2 7 = 3 3 = 4 7 = 5 3 = 67 = 73 = 87 = 93
4 = no others 1 4 = 2 6 = 3 4 = 4 6 = 5 4 = 66 = 74 = 86 = 94
5 = no others 1 5 = 2 5 = 3 5 = 4 5 = 5 5 = 65 = 75 = 85 = 95
6 = no others 1 6 = 2 4 = 3 6 = 4 4 = 5 6 = 64 = 76 = 84 = 96
7 = no others 1 7 = 2 3 = 3 7 = 4 3 = 5 7 = 63 = 77 = 83 = 97
8 = no others 1 8 = 2 2 = 3 8 = 4 2 = 5 8 = 62 = 78 = 82 = 98
9 = no others 1 9 = 2 1 = 3 9 = 4 1 = 5 9 = 61 = 79 = 81 = 99
Delete the tens digit, like follow:
0 = no others 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
1 = no others 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1
2 = no others 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2
3 = no others 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3
4 = no others 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4
5 = no others 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5
6 = no others 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6
7 = no others 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7
8 = no others 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8
9 = no others 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9
So there is no rules to 0,
20 = no others
answered Mar 25 at 6:10
user58107user58107
212
$endgroup$
1
$begingroup$
Keep going, @user58107! It's simpler than that.
$endgroup$
– humn
Mar 25 at 6:42
2
$begingroup$
look the column, my English very poor, can't explain clarification.
$endgroup$
– user58107
Mar 25 at 6:46
$begingroup$
Oh, oh oh oh, @user58107, this puzzle relies on English. (Big give-away.) Thank you for hitching the ride.
$endgroup$
– humn
Mar 25 at 6:52
1
$begingroup$
@humn Maybe a language tag then?
$endgroup$
– Rubio♦
Apr 6 at 4:07
$begingroup$
Right, @Rubio,languagetag added. I was trying to not give away that aspect but did in the comment above and the time is ripe anyway.
$endgroup$
– humn
Apr 7 at 3:11
add a comment |
$begingroup$
0 = no others 10 = no others 20 = no others
1 = no others 1 1 = 2 9 = 3 1 = 4 9 = 5 1 = 69 = 71 = 89 = 91
2 = no others 1 2 = 2 8 = 3 2 = 4 8 = 5 2 = 68 = 72 = 88 = 92
3 = no others 1 3 = 2 7 = 3 3 = 4 7 = 5 3 = 67 = 73 = 87 = 93
4 = no others 1 4 = 2 6 = 3 4 = 4 6 = 5 4 = 66 = 74 = 86 = 94
5 = no others 1 5 = 2 5 = 3 5 = 4 5 = 5 5 = 65 = 75 = 85 = 95
6 = no others 1 6 = 2 4 = 3 6 = 4 4 = 5 6 = 64 = 76 = 84 = 96
7 = no others 1 7 = 2 3 = 3 7 = 4 3 = 5 7 = 63 = 77 = 83 = 97
8 = no others 1 8 = 2 2 = 3 8 = 4 2 = 5 8 = 62 = 78 = 82 = 98
9 = no others 1 9 = 2 1 = 3 9 = 4 1 = 5 9 = 61 = 79 = 81 = 99
Delete the tens digit, like follow:
0 = no others 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
1 = no others 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1
2 = no others 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2
3 = no others 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3
4 = no others 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4
5 = no others 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5
6 = no others 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6
7 = no others 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7
8 = no others 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8
9 = no others 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9
So there is no rules to 0,
20 = no others
answered Mar 25 at 6:10
user58107user58107
212
$endgroup$
1
$begingroup$
Keep going, @user58107! It's simpler than that.
$endgroup$
– humn
Mar 25 at 6:42
2
$begingroup$
look the column, my English very poor, can't explain clarification.
$endgroup$
– user58107
Mar 25 at 6:46
$begingroup$
Oh, oh oh oh, @user58107, this puzzle relies on English. (Big give-away.) Thank you for hitching the ride.
$endgroup$
– humn
Mar 25 at 6:52
1
$begingroup$
@humn Maybe a language tag then?
$endgroup$
– Rubio♦
Apr 6 at 4:07
$begingroup$
Right, @Rubio,languagetag added. I was trying to not give away that aspect but did in the comment above and the time is ripe anyway.
$endgroup$
– humn
Apr 7 at 3:11
add a comment |
$begingroup$
0 = no others 10 = no others 20 = no others
1 = no others 1 1 = 2 9 = 3 1 = 4 9 = 5 1 = 69 = 71 = 89 = 91
2 = no others 1 2 = 2 8 = 3 2 = 4 8 = 5 2 = 68 = 72 = 88 = 92
3 = no others 1 3 = 2 7 = 3 3 = 4 7 = 5 3 = 67 = 73 = 87 = 93
4 = no others 1 4 = 2 6 = 3 4 = 4 6 = 5 4 = 66 = 74 = 86 = 94
5 = no others 1 5 = 2 5 = 3 5 = 4 5 = 5 5 = 65 = 75 = 85 = 95
6 = no others 1 6 = 2 4 = 3 6 = 4 4 = 5 6 = 64 = 76 = 84 = 96
7 = no others 1 7 = 2 3 = 3 7 = 4 3 = 5 7 = 63 = 77 = 83 = 97
8 = no others 1 8 = 2 2 = 3 8 = 4 2 = 5 8 = 62 = 78 = 82 = 98
9 = no others 1 9 = 2 1 = 3 9 = 4 1 = 5 9 = 61 = 79 = 81 = 99
Delete the tens digit, like follow:
0 = no others 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
1 = no others 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1
2 = no others 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2
3 = no others 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3
4 = no others 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4
5 = no others 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5
6 = no others 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6
7 = no others 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7
8 = no others 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8
9 = no others 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9
So there is no rules to 0,
20 = no others
answered Mar 25 at 6:10
user58107user58107
212
$endgroup$
0 = no others 10 = no others 20 = no others
1 = no others 1 1 = 2 9 = 3 1 = 4 9 = 5 1 = 69 = 71 = 89 = 91
2 = no others 1 2 = 2 8 = 3 2 = 4 8 = 5 2 = 68 = 72 = 88 = 92
3 = no others 1 3 = 2 7 = 3 3 = 4 7 = 5 3 = 67 = 73 = 87 = 93
4 = no others 1 4 = 2 6 = 3 4 = 4 6 = 5 4 = 66 = 74 = 86 = 94
5 = no others 1 5 = 2 5 = 3 5 = 4 5 = 5 5 = 65 = 75 = 85 = 95
6 = no others 1 6 = 2 4 = 3 6 = 4 4 = 5 6 = 64 = 76 = 84 = 96
7 = no others 1 7 = 2 3 = 3 7 = 4 3 = 5 7 = 63 = 77 = 83 = 97
8 = no others 1 8 = 2 2 = 3 8 = 4 2 = 5 8 = 62 = 78 = 82 = 98
9 = no others 1 9 = 2 1 = 3 9 = 4 1 = 5 9 = 61 = 79 = 81 = 99
Delete the tens digit, like follow:
0 = no others 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
1 = no others 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1
2 = no others 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2
3 = no others 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3
4 = no others 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4
5 = no others 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5 = 5
6 = no others 6 = 4 = 6 = 4 = 6 = 4 = 6 = 4 = 6
7 = no others 7 = 3 = 7 = 3 = 7 = 3 = 7 = 3 = 7
8 = no others 8 = 2 = 8 = 2 = 8 = 2 = 8 = 2 = 8
9 = no others 9 = 1 = 9 = 1 = 9 = 1 = 9 = 1 = 9
So there is no rules to 0,
20 = no others
answered Mar 25 at 6:10
user58107user58107
212
edited Mar 25 at 6:36
answered Mar 25 at 6:10
user58107user58107
212
answered Mar 25 at 6:10
user58107user58107
212
answered Mar 25 at 6:10
user58107user58107
212
212
1
$begingroup$
Keep going, @user58107! It's simpler than that.
$endgroup$
– humn
Mar 25 at 6:42
2
$begingroup$
look the column, my English very poor, can't explain clarification.
$endgroup$
– user58107
Mar 25 at 6:46
$begingroup$
Oh, oh oh oh, @user58107, this puzzle relies on English. (Big give-away.) Thank you for hitching the ride.
$endgroup$
– humn
Mar 25 at 6:52
1
$begingroup$
@humn Maybe a language tag then?
$endgroup$
– Rubio♦
Apr 6 at 4:07
$begingroup$
Right, @Rubio,languagetag added. I was trying to not give away that aspect but did in the comment above and the time is ripe anyway.
$endgroup$
– humn
Apr 7 at 3:11
add a comment |
1
$begingroup$
Keep going, @user58107! It's simpler than that.
$endgroup$
– humn
Mar 25 at 6:42
2
$begingroup$
look the column, my English very poor, can't explain clarification.
$endgroup$
– user58107
Mar 25 at 6:46
$begingroup$
Oh, oh oh oh, @user58107, this puzzle relies on English. (Big give-away.) Thank you for hitching the ride.
$endgroup$
– humn
Mar 25 at 6:52
1
$begingroup$
@humn Maybe a language tag then?
$endgroup$
– Rubio♦
Apr 6 at 4:07
$begingroup$
Right, @Rubio,languagetag added. I was trying to not give away that aspect but did in the comment above and the time is ripe anyway.
$endgroup$
– humn
Apr 7 at 3:11
1
1
$begingroup$
Keep going, @user58107! It's simpler than that.
$endgroup$
– humn
Mar 25 at 6:42
$begingroup$
Keep going, @user58107! It's simpler than that.
$endgroup$
– humn
Mar 25 at 6:42
2
2
$begingroup$
look the column, my English very poor, can't explain clarification.
$endgroup$
– user58107
Mar 25 at 6:46
$begingroup$
look the column, my English very poor, can't explain clarification.
$endgroup$
– user58107
Mar 25 at 6:46
$begingroup$
Oh, oh oh oh, @user58107, this puzzle relies on English. (Big give-away.) Thank you for hitching the ride.
$endgroup$
– humn
Mar 25 at 6:52
$begingroup$
Oh, oh oh oh, @user58107, this puzzle relies on English. (Big give-away.) Thank you for hitching the ride.
$endgroup$
– humn
Mar 25 at 6:52
1
1
$begingroup$
@humn Maybe a language tag then?
$endgroup$
– Rubio♦
Apr 6 at 4:07
$begingroup$
@humn Maybe a language tag then?
$endgroup$
– Rubio♦
Apr 6 at 4:07
$begingroup$
Right, @Rubio,
language tag added. I was trying to not give away that aspect but did in the comment above and the time is ripe anyway.$endgroup$
– humn
Apr 7 at 3:11
$begingroup$
Right, @Rubio,
language tag added. I was trying to not give away that aspect but did in the comment above and the time is ripe anyway.$endgroup$
– humn
Apr 7 at 3:11
add a comment |
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2
$begingroup$
Apology for the lack of more specific tags: They would give away the solution.
$endgroup$
– humn
Mar 24 at 18:08
6
$begingroup$
Hurray, a humn puzzle! It's been a while.
$endgroup$
– Rand al'Thor
Mar 24 at 19:06
1
$begingroup$
Is there a way to "watch" a question so that I'm notified of new or accepted answers? I've already starred it.
$endgroup$
– MooseBoys
Mar 27 at 1:04
1
$begingroup$
To be clear, is the relation really only meaningful for numbers 0 thru 99, or are you just saying all numbers outside that range would be "no others"?
$endgroup$
– MooseBoys
Mar 27 at 1:07
$begingroup$
Thank you, @MooseBoys. Yes the relation only has relevance to numbers 0 through 99. "No others" would indeed be a great catch-all for other numbers.
$endgroup$
– humn
Mar 27 at 12:17