Tiling with punctured intervals

It was shown by Gruslys, Leader and Tan that any finite subset of ${\mathbb{Z}}^n$ tiles ${\mathbb{Z}}^d$ for some $d$. The first non-trivial case is the punctured interval, which consists of the interval ${-k,\ldots,k} \subset $\mathbb{Z}$$withitsmiddlepointremoved:theyshowedthatthistiles$$\mathbb{Z}$^d$for$d = 2k^2$, and they asked if the dimension needed tends to infinity with $k$. In this note we answer this question: we show that, perhaps surprisingly, every punctured interval tiles ${\mathbb{Z}}^4$.