Henry Ernest Dudeney/Modern Puzzles/119 - Tessellated Pavements

by : $119$

 * 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.


 * Dudeney-Modern-Puzzles-119.png


 * 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?