Henry Ernest Dudeney/Modern Puzzles/119 - Tessellated Pavements

Modern Puzzles by Henry Ernest Dudeney: $119$

Tessellated Pavements

The reader must often have noticed, in looking at tessellated pavements and elsewhere,

that a square space had sometimes to be covered with square tiles under such conditions that a certain number of the tiles have to be cut in two parts.

A familiar example is shown in the illustration, where a square has been formed with ten square tiles.

As ten is not a square number a certain number of tiles must be cut.

In this case it is six.

It will be seen that the pieces $1$ and $1$ are cut from one tile, $2$ and $2$ from another, and so on.

Now, if you had to cover a square space with exactly twenty-nine square tiles of equal size, how would you do it?

What is the smallest number of tiles that you need cut in two parts?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Patchwork Puzzles: $119$. -- Tessellated Pavements
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Dissection Puzzles: $342$. Tessellated Pavements