IBM挑战2005年5月：大理石及玻璃砖英文原文如下：Part 1:Imagine a rectangular grid of compartments, of size 68 by 122. That's 8,296 compartments. Suppose we had 8,290 black marbles and were to place them in compartments, at most one marble per compartment, in such a way that each row and each column would have an even number of marbles. How many ways could this be done?Part 2:Imagine 6 little clear glass cubes with dimensions of 1x1x1. Imagine 90 more just like them except these 90 have a pretty little bright red sphere at their center; the spheres have a radius of 1/10. So, all together we have 96 little 1x1x1 cubes.Now let's arrange these 96 into a block with dimensions of 4x4x6 so that in any column (up and down) or row (left to right) or (front to back) there is an even number of small cubes with the red centers. Zero is an even number.How many ways would there be to do this?大概意思如下：第一部份把8290块黑色大理石放在68行122列共8296个格子中，每一个格子至多放1块。要每一行及每一列的大理石数目都是偶数，有多少种放置方式？第二部份有96块玻璃砖，其中90块砖的中央有红色珠子，另外6块则无。把这些玻璃砖摆放成4x4x6的长方体，要每一行、每一列及每一柱的珠子数目都是偶数，有多少种放置方式？