Toying Around I
Probability
Level
3
A manufacturer makes blocks for children, each block being a two inch cube whose faces are painted one of two colors, blue and red. Some blocks are all blue, some all red, and some have a mixture of blue and red faces. How many different kinds of blocks can the manufacturer make?
The answer is 10.
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1 solution
6R 0B , 6B 0R - 1 (for both cases as they are symmetrical); 5R 1B , 5B 1R - 1 ; 4R 2B , 4B 2R - 2 ( as the two same colored faces can be either adjacent or opposite); 3R 3B - 2 ( as the three same colored faces can either be sharing a single corner, or be such that two faces are opposite); Thus, 2(1+1+2) + 2 = 10