Primes and squares in a grid

Question

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.

$\begingroup$ Are leading zeroes permitted? $\endgroup$
– hexomino
Feb 28, 2021 at 23:41 — hexomino, Feb 28, 2021 at 23:41
$\begingroup$ No leading zeros! $\endgroup$
– Bernardo Recamán Santos
Feb 28, 2021 at 23:48 — Bernardo Recamán Santos, Feb 28, 2021 at 23:48

Stiv · Accepted Answer · 2021-03-01 09:10:58Z

2

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!

Stiv

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answered Mar 1, 2021 at 8:45

Laska

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Vassilis Parassidis · Accepted Answer · 2021-03-01 02:11:31Z

-2

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

590080113475142976

answered Mar 1, 2021 at 0:40

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1

$\begingroup$ May we see one of each! $\endgroup$
– Bernardo Recamán Santos
Mar 1, 2021 at 1:18
1

$\begingroup$ I added a picture to my answer. $\endgroup$
– Vassilis Parassidis
Mar 1, 2021 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, 2021 at 7:32
$\begingroup$ I think the downvotes may be because someone doesn't have a sense of humor. $\endgroup$
– Penguino
Mar 1, 2021 at 22:56

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2 Answers 2