Henry Ernest Dudeney/Modern Puzzles/119 - Tessellated Pavements/Solution

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?

Solution

The illustration shows how the square space may be covered with twenty-nine square tiles,

by laying down seventeen whole tiles and cutting each of the remaining twelve tiles in two parts.

Two parts having the same number form a whole tile.

Sources

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