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3 cubes Painted

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3 cubes Painted

by deepoe » Wed Mar 04, 2009 9:26 am
How many different ways can 3 cubes be painted if each cube is painted one color and only the 3 colors red, blue and green are available? ( order is not considered, for example, green, green, blue is considered the same as green, blue green. )


A. 2
B. 3
C. 9
D. 10
E. 27

Is there any fast solution for this one?
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by DanaJ » Wed Mar 04, 2009 9:39 am
The way I see it:
1. You've got three cases of "mono-color": RRR, GGG, BBB
2. Think of the case when you've got two cubes of the same color and the other one of a different color: there will be 3*2 = 6 such cases, since you've got three colors in total and two other options once you've already picked the other one
3. Last but not least: RGB or all the colors case

This makes 2 + 6 + 1 = 10 IMHO.
There might be an easier way with combinatorics/permutations, but I prefer to avoid this when I can, since I HATE them....
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by kamu » Wed Mar 04, 2009 10:45 am
Try Different colors first.
RGB

The Try for Doubles + 1
RR (R+G+B)
BB (R+G+B)
GG (R+G+B)

total = 10
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