Consecutive Seven

#ConsecutiveSeven

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 6 years, 2 months ago

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 - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$