Thumps Up

Call a set of unit squares a Thumps-up sign if it is obtained by cutting an unit square on a corner of a $2 \times m$ rectangle. For example, a single unit square and a L-tromino are both Thumps-up signs. Let $n \ge 1$ be an integer. Find the smallest number $k$ such that there exist a partition of a $2n \times 2n$ square into $k$ Thumps-up signs.

#Combinatorics

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

is it 2n?

Dorra Hamza - 1 year, 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}`	$\boxed{123}$