B1. The solution to each clue of this crossnumber is a two-digit number, that does not begin with a zero.

Find all the different ways in which the crossnumber can be completed correctly.
Across
Down
1. A prime
1. A square
3. A square
2. A square
Solution
First note that the only units digits of two-digit squares are 1, 4, 5, 6 and 9 . As 3 across is a square composed of two such digits, its only possible values are 16, 49 and 64. If 3 across is 16 , then 1 down is 81 and 2 down is either 16 or 36 . In turn, 1 across is 81 or 83 . Of these, only 83 is prime so there is exactly one way of completing the crossnumber when 3 across is 16 .
Alternatively, if 3 across is 49 then 1 down is 64 and 2 down is 49 . However, this makes 1 across 64 , which is not prime.

Finally, if 3 across is 64 then 1 down is 16 or 36 and 2 down is 64 . This means 1 across is 16 or 36 , neither of which is prime.

Therefore there is exactly one way of completing the crossnumber, as shown.