"X = 34

In each column, the middle number divided by the top number yields the bottom number; the decimal point is removed from the answer. Therefore, 7/2=35(3.5), 8/5=16(1.6), 9/8=1125(1.125), and 17/5=34(3.4)."

We had a number of other answers, the most common of which was 8704. Here is one person's explanation for this answer:

"The first half of the puzzle sets the pattern. Multiplying diagonally, 5 x 7 = 35 and 2 x 8 = 16. The second half has a twist by cubing the first number, 5 ^ 3 x 9 = 1125, so 8 ^ 3 x 17 = 8704."

While this is as good a guess as any, there would be only one incidence of cubing given the information available, which is because it is a coincidence, as is the diagonal multiplication. You have 2 incidents of 1 thing (diagonal multiplication in first 2 sets), 1 incident of something else (cubing of 1 number, then diagonal multiplication). To assume the 4th item would use the same function as the 3rd is conjecture, although a good guess. The actual solution shows 3 incidents of one systematic thing. The 4th item perfectly follows suit with the previous 3 items, thus making it the most logical answer. This was a tough problem.

Winner: Shirley Wolf, Rockville, MD.

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