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This is an entry for the 16th Fortnightly Challenge.


Jim : Bob, I have solved the puzzle !!
Bob : I do not believe you, show me !
Jim : No, you have to solve it yourself.

After some discussion between them how Jim can prove that he has solved the puzzle without showing Bob the answer. Jim cuts his answering paper into pieces, then Jim shows a set of numbers.

Jim : look these numbers, they are all unique right ?

Jim does that more than 20 times

What puzzle had Jim solved ?

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3
  • $\begingroup$ Are the grammar errors intentional or not?? $\endgroup$
    – Sid
    Sep 30, 2016 at 10:19
  • $\begingroup$ no, you can help me fix the grammar error. $\endgroup$ Sep 30, 2016 at 10:20
  • $\begingroup$ @JamalSenjaya : Oh ! He is showing the same number 20 times ? (Another joke: Both are mad) $\endgroup$
    – user27395
    Sep 30, 2016 at 10:31

1 Answer 1

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I think the puzzle is

a sudoku

The numbers jim shows are

the numbers 1 to 9 of each column, row and 3x3 block

More than 20 times, because

a sudoku has 9 columns + 9 rows + 9 blocks = 27 combinations of 1 to 9

Jim asks if the numbers are unique, because

a sudoku has in every row, column and block the numbers 1 to 9 uniquely

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  • $\begingroup$ The number of solutions to a Sudoku is 1. How can the guy show 20 combination of numbers without violating the rules?? $\endgroup$
    – Sid
    Sep 30, 2016 at 10:45
  • $\begingroup$ He does only need to show the numbers of a row, column or bloack and not their order in the puzzle. $\endgroup$
    – Meta45
    Sep 30, 2016 at 10:46
  • $\begingroup$ Ohh, I get it. He cut up the paper... Thanks.. $\endgroup$
    – Sid
    Sep 30, 2016 at 10:48
  • 4
    $\begingroup$ This may very well be right, but as it stands it doesn't at all prove that Jim has solved the puzzle. Suppose e.g. he has solved a completely different Sudoku puzzle; then his solution will still have the required properties. And if Bob doesn't get to see anything other than the bits Jim shows him, he has no way to know that Jim isn't rearranging the pieces in cheaty ways. $\endgroup$
    – Gareth McCaughan
    Sep 30, 2016 at 11:05
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    $\begingroup$ The first problem is resolved if we suppose that the answer sheet has the "clues" printed indelibly on it, and the second if we suppose e.g. that Bob gets to choose at each step which row, column or block Jim will show him the numbers from next. $\endgroup$
    – Gareth McCaughan
    Sep 30, 2016 at 11:06

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