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|
+--+--+--+--+--+

(In reply to a solution by SilverKnight)

{2,3,8} #3 sum 13;

{1,6,7,11,12} #5 sum 37;

{4,5,10} #3 sum 19;

{16,21,22} #3 sum 59;

{9,13,14,15,17,18,19,20,23,24,25} #11 sum 197;

Posted by goFish on 2005-10-25 21:01:59