IBM Ponder This #085 · May 2005

Puzzle for May 2005

This month's puzzle comes from Gale Greenlee.
Both parts need to be solved.

We have received 100 correct solutions for the May puzzle.
The list of correct solvers is now closed.
The solution will be posted soon.

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?

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The first 100 people who answer correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

Solution

Best opened after a real attempt

To be added.