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Seven Dwarfs

Stage: 3 Short Challenge Level: Challenge Level:1
Suppose the youngest dwarf is $x$ years old. The sum of the ages of the youngest three is $x+(x+1)+(x+2)=3x+3$, and the sum of the ages of the oldest three is $(x+4)+(x+5)+(x+6)=3x+15$.

We know that $3x+3=42$, so $3x+15=42+12=54$.

This problem is taken from the UKMT Mathematical Challenges.
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