I Wonder Why - 34

Take the numbers 1 through 16 and write them into a 4 x 4 grid like so:

1	2	3	4
5	6	7	8
9	10	11	12
13	14	15	16

Now choose a random number in the grid and circle it. Mark out the rest of the numbers in the same row and column.
Do this three times total and you should have one number left. Circle it.

Sum the four numbers you have circled. Why does the sum always equal 34?

Answer: By choosing this way we are picking 4 numbers that do not share rows or columns. The sum of the first column is 1+5+9+13 = 28, but by forcing picks 1, 2 and 3 columns to the right for each row the sum is forced to be 28+1+2+3 = 34.