Problem 359, Hilbert's new Hotel Had no idea where to start at all, the only thing I could was to write a small program to print out first hundred numbers in naive way. [ 1 , 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91] [ 2 , 7, 9, 16, 20, 29, 35, 46, 54, 67, 77, 92] [ 4 , 5, 11, 14, 22, 27, 37, 44, 56, 65, 79, 90] [ 8 , 17, 19, 30, 34, 47, 53, 68, 76, 93] [ 12 , 13, 23, 26, 38, 43, 57, 64, 80, 89] [ 18 , 31, 33, 48, 52, 69, 75, 94] [ 24 , 25, 39, 42, 58, 63, 81, 88] [ 32 , 49, 51, 70, 74, 95] [ 40 , 41, 59, 62, 82, 87] [ 50 , 71, 73, 96, 100] [ 60 , 61, 83, 86] [ 72 , 97, 99] [ 84 , 85] [ 98 ] As you may see, the result is very interesting. The numbers on the first column seems to be ( row + 1 ) / 2 * ( row / 2 ) * 2. Note that row/2*2 != row since all operations are integer operations. If we calculate the delta values between consecutive numbers in each row, we got 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, 13, 5 , 2 , 7, 4 , 9, 6 ,11, 8 ,13, 10 , 15, ...
I'm almost certain you will not find anything useful here in this blog.