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
possible subsets by Charlie)
Largest prime (for a size 13 subset) is 241 which is made of all the squares from 11 to 25 except 12 and 17.
...which is interesting but not very useful since it goes nowhere from there as a solution. :)
re: possible subsets
