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Consecutive Seven

Note by Llewellyn Sterling
2 years, 8 months ago

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The subsets are:

\[\begin{array} {ccc} \text{Subset} & \text{The 3 numbers} & \text{Sum of 3 numbers} \\ 1 & 0 \quad 7 \quad 20 & 27 \\ 2 & 1 \quad 8 \quad 19 & 28 \\ 3 & 2 \quad 9 \quad 18 & 29 \\ 4 & 3 \quad 10 \quad 17 & 30 \\ 5 & 4 \quad 11 \quad 16 & 31 \\ 6 & 5 \quad 12 \quad 15 & 32 \\ 7 & 6 \quad 13 \quad 14 & 33 \end{array} \]

Chew-Seong Cheong - 2 years, 8 months ago

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They can also be:

\(\quad Subset\quad \quad \\ \begin{matrix} 6 & 7 & 14 \\ 5 & 8 & 15 \\ 4 & 9 & 16 \\ 3 & 10 & 17 \\ 2 & 11 & 18 \\ 1 & 12 & 19 \\ 0 & 13 & 20 \end{matrix}\)

Multiple answers. The first and last elements of each subset above can be interchanged with the respective first and last element of any other subset(since the first and last element of each subset adds to \(20\)). Already giving us \(7!=5040\) different distributions of subsets.

Raghav Vaidyanathan - 2 years, 8 months ago

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