If you have been on Facebook at all over the last year, you have probably seen the “puzzle” where there is a grid, and the question reads “How many squares do you see?” Some people (clearly not readers of this blog) only count the 1×1 squares, and not the 2×2, 3×3, 4×4 or larger squares.
Some numbers, when squared, are palindromes: 112 is 121, and 262 is 676. Other numbers are the sums of sets of consecutive squares: 92 + 102 = 181, and 42 + 52 + 62 = 77.
This week’s puzzle is simple: How many numbers between 1 million and 10 million are both palindromes and the sums of sets of consecutive squares?
(NOTE: For purposes of this puzzle, please consider only sums of sets of squares of positive integers.)