Problems & Puzzles: Puzzles

Puzzle 965. Partitioning an 8x8 square

Fausto Morales sent the following nice puzzle:

Find the unique partition of the 8x8 square below into the 10 smallest primes containing digits 1 and 9 only, so that each prime appears once left-to-right and once top-to-bottom.

1 9 9 9 1 9 9 1
9 1 1 1 1 9 1 9
1 1 9 1 1 1 1 9
9 9 1 1 1 1 1 9
9 1 9 9 1 9 1 1
9 9 1 9 1 9 9 9
1 9 9 1 9 9 1 1
1 9 1 9 1 9 9 9

The 10 smallest primes mentioned above are;

11, 19, 191, 199, 911, 919, 991, 1999, 9199, 11119

A solved example:

If the 8x8 matriz is:

1 9 1 9 9 9 1 1
9 1 1 9 1 9 9 9
9 1 9 1 9 1 9 1
9 1 1 1 9 9 1 9
1 1 1 1 1 1 9 1
9 9 1 1 9 9 9 9
9 1 1 1 1 9 1 9
1 9 9 9 1 9 1 9

The solution is this one:

 1 9 1 9 9 9 1 1 9 1 1 9 1 9 9 9 9 1 9 1 9 1 9 1 9 1 1 1 9 9 1 9 1 1 1 1 1 1 9 1 9 9 1 1 9 9 9 9 9 1 1 1 1 9 1 9 1 9 9 9 1 9 1 9

Contributions came from Michael Hürter, Oscar Volpatti

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Michael wrote on Aug 10, 2019:

 1 9 9 9 1 9 9 1 9 1 1 1 1 9 1 9 1 1 9 1 1 1 1 9 9 9 1 1 1 1 1 9 9 1 9 9 1 9 1 1 9 9 1 9 1 9 9 9 1 9 9 1 9 9 1 1 1 9 1 9 1 9 9 9

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Oscar wrote on Aug 12, 2019:

This is my four-coloured solution, with five partitions and sixteen digits per colour:

1 9 9 9 1 9 9 1
9 1 1 1 1 9 9
1 1 9 1 1 1 1 9
9 1 1 1 1 1 9
9 9 1 9 1 1
9 1 9 1 9 9 9
1 9 9 1 9 9 1 1
1 9 1 9 1 9 9 9

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