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# rocdocmac

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2. ## 3-color cube

Oooops, really slipped up here! Fifty seven appears to be the correct answer. Attached the updated solution with the two addtional arrangements added to the bottom row on the right. My sincere apology to all participants. Colored cube.xlsx
3. ## 3-color cube

If each side of a tetrahedron is an equilateral triangle painted white or black, five distinct color patterns are possible: (1) all sides white, (2) all black, (3) just one side white and the rest black, (4) just one side black and the rest white, and (5) two sides white, while the other two are black. If each side of a cube is painted red or blue or yellow, how many distinct color patterns are possible?
4. ## 3-color cube

Colored cube.xlsx

6. ## The clock setter

Did Stefan only glance at his friend's wall clock as he entered the house, but not when he left?

8. ## Chess Board Puzzle

Use the twelve pieces on the left to create a chess board, The pieces may be flipped!

17. ## Chess Board Puzzle

... rotate and/or flip!
18. ## Two people cross a river

Conjoined twins?

21. ## Mouse & Cheese Cube

Hopefully this one has not appeared before... Suppose 27 identical cubical chunks of cheese are piled together to form a cubical stack, as illustrated below. What is the maximum number of these cheese chunks through which a mouse of negligible size could munch before exiting the stack, assuming that the mouse always travels along the grid of 27 straight lines that pass through the centers of the chunks parallel or perpendicular to their sides, always makes a 90 degree turn at the center of each chunk it enters, and never enters any chunk more than once?

24. ## Mouse & Cheese Cube

Have another go!

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