The numbers from 1 to 9 are arranged in a 3×3 grid:
a b c
d e f
g h i
- The corner numbers are all odd.
- One diagonal sums to 20, and its numbers ascend from left to right.
- All of the numbers in one column are squares.
- One row sums to 20, and its numbers ascend from left to right.
- All of the numbers in one column are primes.
- In one row, one of the numbers is the product of the other two.
- One column’s numbers are consecutive (though not necessarily in order).
- a = 3.
What are the values of a through i?
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, June 26, 2013 at noon Pacific Time. I will post the answer shortly after.