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Start with the set of the twenty-one numbers $0$ - $20$.


numbers from 0 to 20

 

 

Can you arrange these numbers into seven subsets each of three numbers so that when the numbers in each are added together, they make seven consecutive numbers?

For example, one subset might be $\{2, 7, 16\}$

$2 + 7 + 16 = 25$

another might be $\{4, 5, 17\}$

$4 + 5 + 17 = 26$

As $25$ and $26$ are consecutive numbers these sets are the kind of thing that you need.

[Remember that consecutive numbers are numbers which follow each other when you are counting, for example, $4$, $5$, $6$, $7$ or $19$, $20$, $21$, $22$, $23$.]

 

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