Question 187
Find the minimal natural number $n$ with the following property: It is possible to tile the plane with squares whose side lengths belong to the set $\{1,2, \ldots, n\}$ so that no two squares with the same side length touch along a segment of an edge.
Remark. Squares with the same side length can touch at a vertex, however. Not all of the side lengths from $1$ to $n$ need to be used in the tiling.
Figure 1
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Figure 4
Remark. Squares with the same side length can touch at a vertex, however. Not all of the side lengths from $1$ to $n$ need to be used in the tiling.
Figure 1
Figure 2
Figure 3
Figure 4