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So I was given this puzzle quite some time ago and just thought it would make a nice addition to this site:

Your task is to determine the method how the result is determined from the given number. A few example cases include:

177383 -> 2
267453 -> 2
111111 -> 0
636240 -> 4
367183 -> 3
247123 -> 1
369108 -> 5

To those, who hit a brick wall, here is a tip: This puzzle is easiest for young children and gets harder the older you get... Happy guessing ;)

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    $\begingroup$ Nice hint. It is really great. $\endgroup$
    – Always Confused
    Jan 28, 2017 at 9:52

3 Answers 3

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The number is the

number of "holes" in the written decimal representation of the number.

More specifically,

each digit contributes this much to the total number:

  • 0: 1
  • 1: 0
  • 2: 0
  • 3: 0
  • 4: 0 or 1, depending on how you draw them
  • 5: 0
  • 6: 1
  • 7: 0
  • 8: 2
  • 9: 1

In your case above,

4 is drawn with a hole, so it contributes 1.

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    $\begingroup$ No spoiler here because there really isn't much I could leave exposed if I did choose to hide all the important details. $\endgroup$
    – user88
    Nov 30, 2014 at 17:56
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    $\begingroup$ This is right, but 0 has 2 holes, at least in the font used. I'm kind of surprised that you got it right even with this happening. $\endgroup$
    – mdc32
    Nov 30, 2014 at 17:57
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    $\begingroup$ It's more a function of having seen these puzzles before. They're chestnuts. $\endgroup$
    – user88
    Nov 30, 2014 at 17:57
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    $\begingroup$ @mdc32: on the font that I'm using, 0 has only a single hole. $\endgroup$
    – user88
    Nov 30, 2014 at 17:57
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    $\begingroup$ I like the puzzle, but I would do away with the "harder the older you get" hint. That makes it too easy, because one immediately disregards maths. Maybe edit it? $\endgroup$
    – BmyGuest
    Nov 30, 2014 at 19:11
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I included mathematics :)

The method is as follows:

  1. Add all the digits
  2. If step 1's result has a 9, subtract 2
  3. If step 1's result has a 6, add 1
  4. If the original number has a 0, multiply by 2 then subtract 4
  5. Add all the digits
  6. Mod 7 step 5's result

Now use this method on your numbers:

1 + 7 + 7 + 3 + 8 + 3 = 29
29 - 2 = 27
2 + 7 = 9
9 % 7 = 2

2 + 6 + 7 + 4 + 5 + 3 = 26
26 + 1 = 27
2 + 7 = 9
9 % 7 = 2

1 + 1 + 1 + 1 + 1 + 1 = 6
6 + 1 = 7
7 = 7
7 % 7 = 0

6 + 3 + 6 + 2 + 4 + 0 = 21
21 x 2 - 4 = 38
3 + 8 = 11
11 % 7 = 4

3 + 6 + 7 + 1 + 8 + 3 = 28
2 + 8 = 10
10 % 7 = 3

2 + 4 + 7 + 1 + 2 + 3 = 19
19 - 2 = 17
1 + 7 = 8
8 % 7 = 1

3 + 6 + 9 + 1 + 0 + 8 = 27
2 x 27 - 4 = 50
5 + 0 = 5
5 % 7 = 5

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  • $\begingroup$ Not what I was looking for, but creative :D $\endgroup$
    – ThreeFx
    Dec 1, 2014 at 7:16
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    $\begingroup$ @ThreeFx damnit :D $\endgroup$
    – Abraham Zhang
    Dec 1, 2014 at 7:27
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    $\begingroup$ In general, when the number of rules is equal or close to the number of cases, then the rules are made up to fit the data. $\endgroup$
    – Florian F
    Dec 1, 2014 at 8:24
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    $\begingroup$ I know this is for fun, but your equation breaks on 600000 :) +1 for you $\endgroup$
    – Brian J
    May 8, 2015 at 19:11
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There is a simple rule.

Reduce the number mod 1014, then mod 120 and finally mod 7

177383 -> 947 -> 107 -> 2
267453 -> 771 -> 51 -> 2
111111 -> 585 -> 105 -> 0
636240 -> 462 -> 102 -> 4
367183 -> 115 -> 115 -> 3
247123 -> 721 -> 1 -> 1
369108 -> 12 -> 12 -> 5

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  • $\begingroup$ And who says puzzlers don’t have a sense of humour. Cheers! $\endgroup$
    – Will Octagon Gibson
    Oct 3 at 2:52

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