Tuesday, March 22, 2011

Arrange 20 cubes in 4 piles using these clues:

All piles contain an even number of cubes.there are twice as many cubes in the first pile as in the 2nd pile. the largest number of cubes are in the first pile. all piles have different number of cubes. each pile has at least one cube.how many cubes in pile1,pile2,pile3,pile4????

Pile 2: x number of cubes
Pile 1: 2x
Each pile must have at least 2 cubes to have an even number.

x + 2x = 3x
3x < 20 so x < 6.67

Using trial and error, if pile 2 had 6 cubes and pile 3 had 12 cubes, there would be 2 cubes left. You can't make two piles with 2 cubes, because one is not an even number. If pile 2 had 5 cubes and pile 1 had 10 cubes, there would be 5 cubes left. This is an odd number and can't be divided into two even numbered piles. If pile 2 had 4 cubes and pile 1 had 8 cubes, there would be 8 cubes left. This can then be split into a piles of 2 and 6.

Pile 1: 8
Pile 2: 4
Pile 3: 6
Pile 4: 2

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