# Primes and squares in a grid

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?

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

• Are leading zeroes permitted? Feb 28, 2021 at 23:41
• No leading zeros! Feb 28, 2021 at 23:48

## 2 Answers

I think there is a unique answer for the squares:

8-169-225-1
484-625-729
1-441-676-6

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

590080113475142976

• May we see one of each! Mar 1, 2021 at 1:18
• I added a picture to my answer. Mar 1, 2021 at 2:11
• 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?
– Stiv
Mar 1, 2021 at 7:32
• I think the downvotes may be because someone doesn't have a sense of humor. Mar 1, 2021 at 22:56