In the two rows the grids in each row form a pattern, so there are two patterns and they are similar to each other but not the same. One element (either in the upper or lower row) breaks the pattern. Identify that element.

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1 Answer 1


I've come up with a rule per row which describes all the patterns first except one.

For the first row, every pattern except the last can be 'drawn' by starting on a dark square, and moving to any of the eight adjacent squares (N, E, S, W, NE, NW, SE, SW) until all dark squares are visited without visiting the same square twice (A Hamiltonian path for those interested).

The rule for the second row, being similar to the first, is any arrangement for which a Hamiltonian path does not exist when diagonals are not permitted (Only N, E, S, W directions are available). Every pattern except the last matches this rule.

  • $\begingroup$ Doesn't your second rule mean both the first one, third one and the last one are the odd ones out? $\endgroup$
    – Yout Ried
    Oct 6, 2019 at 23:56
  • $\begingroup$ @YoutRied No, the last one is the only pattern with a possible path covering every dark square. I should probably specify that I'm looking at the dark squares. $\endgroup$ Oct 7, 2019 at 0:12
  • $\begingroup$ That makes more sense. $\endgroup$
    – Yout Ried
    Oct 7, 2019 at 0:16

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