Weihnachtsmann rot

Challenge from 22. December

Midoku

Author: Ariane Beier

Project: MATH+ School Activities

Challenge:

Last year, directly after Christmas, elf Sasha was given a Sudoku puzzle by her friend Alex. The puzzle was intended to entertain her on the long train ride from the North Pole to her home town. But, as soon as she sat down in the comfortable train seat and the coach started moving soothingly, she fell asleep—after all, she just had worked her way through a very exhausting Christmas season—and woke up only shortly before arriving at her destination. Thus, Sasha did not even attempt to solve the puzzle.

Back home, Sasha forgot to empty her pants' pockets before putting them into the washing machine. When she hung the pants up to dry, she pulled out a piece of paper with only the following on it:

Although Sasha was pretty sure that there were more digits given on the Sudoku grid before its involuntary bath and roller coaster ride in the washing machine, she was not able to recollect them. However, she did remember the rules of this special Sudoku:

  1. The normal Sudoku rules apply, i. e. every row, every column, and every 3 by 3 subgrid contains the digits from 1 to 9 exactly once.

  2. Any two cells separated by a knight's (see Fig. 1, left) or king's (chess) move (see Fig. 1, center) cannot contain the same digit.

  3. Any two orthogonally adjacent cells (see Fig. 1, right) cannot contain consecutive digits (e. g. not 1 & 2 or 5 & 6).
Figure 1: Special rules of the given Sudoku.
Left: Each y is separated from x by a knight's move.
Center: Each y is separated from x by a king's move.
Right: Every y is orthogonally adjacent to the x.

Always tempted by a tricky challenge, Sasha whipped out her pencil and started to ponder. After 25 minutes of heavy thinking, she was able to finish the Sudoku.

What digit did Sasha write down in the uppermost right corner?

Artwork: Friederike Hofmann

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Possible answers:

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5

  6. 6

  7. 7

  8. 8

  9. 9

  10. Apparently, Sasha made a mistake. The given Sudoku cannot be solved without ambiguity.

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