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Fruit Bowls
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fruit bowl puzzle

A grandmother prepared bowls of fruits for her family. The only fruits available to her were cherries, apricots and red currants. Of course no bowl was empty.

All but five bowls contain some cherries,
all but four contain some apricots, and
all but three contain some red currants.

How many bowls were at the dinner?

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Let X, Y and Z be the number of bowls of fruits and T be the total number of Bowls
X + 5 = T
Y + 4 = T
Z + 3 = T

3T = X + 5 + Y + 4 + Z + 3
3T = (X+Y+Z) + 12
3T = T + 12
T = 6

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