### 3.7.174. Partridge

Denotes the fact that a constraint can be used for solving the Partridge problem: the Partridge problem consists of tiling a square of size $\frac{n·\left(n+1\right)}{2}$ by $\frac{n·\left(n+1\right)}{2}$ squares of respective sizes

• 1 square of size 1,

• 2 squares of size 2,

•  $...$ ,

• $n$ squares of size $n$.

It was initially proposed by R. Wainwright and is based on the identity $1·{1}^{2}+2·{2}^{2}+...+n·{n}^{2}={\left(\frac{n·\left(n+1\right)}{2}\right)}^{2}$. The problem is described in http://mathpuzzle.com/partridge.html. Figure 3.7.39 gives a solution for $n=12$ found with $\mathrm{𝚐𝚎𝚘𝚜𝚝}$.

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