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

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

1,6,7,11,16 (41)
2,3,8,12,13,17,18 (73)
19,21,22,23,24 (109)
9,14,15,20,25 (83)
4,5,10 (19)

Posted by Aravind on 2005-10-26 00:08:54