Each square of the 5x5 grid below contains a number 1-25. Divide the grid into five regions so that the number of squares and the sum of the squares in each region are both odd prime numbers. (1 is not a prime)
For example, the region consisting of {2,3,8} is a valid region. It contains 3 squares (3 is an odd prime) and the sum of the numbers in the squares is prime (2+3+8=13 is an odd prime).

+--+--+--+--+--+
| 1| 2| 3| 4| 5|
+--+--+--+--+--+
| 6| 7| 8| 9|10|
+--+--+--+--+--+
|11|12|13|14|15|
+--+--+--+--+--+
|16|17|18|19|20|
+--+--+--+--+--+
|21|22|23|24|25|
+--+--+--+--+--+

I just played around with it a bit (so there may be other solutions), and I stumbled upon:

+--+--+--+--+--+
| 1| 2  3| 4  5|
+  +     +--+  +
| 6| 7  8  9|10|
+  +--+--+--+--+
|11 12|13 14 15|
+--+  +     +--+
|16|17|18 19|20|
+  +--+--+--+  +
|21 22 23 24 25|
+--+--+--+--+--+

or otherwise written:
1, 6, 11, 12, 17
2, 3, 7, 8, 9
4, 5, 10
13, 14, 15, 18, 19
16, 20, 21, 22, 23, 24, 25

Posted by SilverKnight on 2005-10-25 15:43:51