Each cell in the lower-right 9x9 grid must contain a positive integer or be left blank. Numbers on the outside of the grid indicate the sums of one or more adjacent digits in that row or column, in order. Each sum is separated by at least one blank cell. No number can be repeated in a row or column. There are two possible solutions. You have to work out which one is “correct” and why.

Okay, this is probably not my best creation, but hopefully the humour makes up for the lack of quality 😊

NOTE: This type of puzzle is known as Japanese Sums. If you are unfamiliar with this type of puzzle, a good introduction is available here.

enter image description here

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    $\begingroup$ Just to be clear: Digits 1-9 only? (EDIT: I now see it is impossible to use higher by the sums on the left-hand side - never mind!) $\endgroup$ – Stiv Sep 30 at 10:53
  • $\begingroup$ @Stiv It sounds like you can have any positive integer in a box and there will be gaps like in a nonogram. $\endgroup$ – hexomino Sep 30 at 10:55
  • $\begingroup$ @hexomino Yeah, next time I'll watch the video provided before spewing my thoughts! Thanks. $\endgroup$ – Stiv Sep 30 at 10:57
  • $\begingroup$ Are we supposed to assume the column that's blank on top has no digits in it? $\endgroup$ – msh210 Sep 30 at 12:00
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    $\begingroup$ Here are some great cheating stories for your enjoyment: ssqq.com/archive/cheatingneverwin.htm $\endgroup$ – Dmitry Kamenetsky Oct 2 at 8:02

The answer is:

The final puzzle at the Philadelphia Sudoku Invitational where Eugene Varshavsky cheated. Along with two of the three(maybe?) digits Varshavsky solved (the other was R1C3)

The puzzle:

Givens = Green
Blue = Eugene's Answers in the puzzle
Orange = Eugene's (suspected) answer not in the puzzle
enter image description here

There is another solution... 9s in R35C79 can be swapped without breaking the puzzle as defined. The one provided above is correct (R3C7 and R6C9 filled) because it matches the Varshavsky puzzle. Also, if the 9s were swapped the result would be a Sudoku with 27 solutions.


Eugene Varshavsky is infamous for cheating at a chess tournament and then in a Sudoku Tournament.
Cracking the Cryptic Commentary
Number Warrior Blog
Thomas Snyder Blog


Do you also watch Cracking the Cryptic?

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  • $\begingroup$ Obviously correct answer, but can you prove these are the only two solutions? Also, there are contradictory sources as to rot13(jurgure Rhtrar fbyirq ebj bar pbyhza guerr be abg) $\endgroup$ – happystar Sep 30 at 20:19

I got these solutions:

Solution 1:

Japanese Sums Sln 1

Solution 2:

Japanese Sums Sln 2

Out of these two, I think Solution 1 is likely more correct, because drawing a line across the 5th row would make the shaded black squares horizontally symmetrical.

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