i) Place thirteen different three-digit prime numbers in the empty cells of this grid.

ii) Now place thirteen different three-digit square numbers in the empty cells of this grid.

How many solutions are there of each instance?

Source: https://www.amazon.com/-/es/Bernardo-Recam%C3%A1n/dp/048684241X

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Numbers are to be read as in a crossword: across or down.

  • $\begingroup$ Are leading zeroes permitted? $\endgroup$
    – hexomino
    Feb 28 at 23:41
  • $\begingroup$ No leading zeros! $\endgroup$ Feb 28 at 23:48

I think there is a unique answer for the squares:


If there is a unique answer for the primes too, then I will say bravo!


The number of solutions for squares are 77520 and the number of solutions for primes are



  • 1
    $\begingroup$ May we see one of each! $\endgroup$ Mar 1 at 1:18
  • 1
    $\begingroup$ I added a picture to my answer. $\endgroup$ Mar 1 at 2:11
  • 3
    $\begingroup$ I think the OP is looking for a solution with 1 digit per white cell, like a regular crossword. That way there would be far fewer possibilities than you state here. This probably also explains why you're getting downvotes here. Maybe try again? $\endgroup$
    – Stiv
    Mar 1 at 7:32
  • $\begingroup$ I think the downvotes may be because someone doesn't have a sense of humor. $\endgroup$
    – Penguino
    Mar 1 at 22:56

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