Henry Ernest Dudeney/Modern Puzzles/Geometrical Problems/Patchwork Puzzles

Henry Ernest Dudeney: Modern Puzzles: Geometrical Problems: Patchwork Puzzles

$117$ - The Patchwork Quilt

Here is a patchwork quilt that was produced by two young ladies for some charitable purpose.

When they came to join their work it was found that each lady had contributed a portion that was exactly the same size and shape.

It is an amusing puzzle to discover just where these two portions are joined together.

Can you divide the quilt into two parts, simply by cutting the stitches, so that the portions shall be of the same size and shape?

$118$ - The Improvised Draughts-Board

Some Englishmen at the front during the Great War wished to pass a restful hour at a game of draughts.

They had coins and small stones for the men, but no board.

However, one of them found a piece of linoleum as shown n the illustration,

and, as it contained the right number of squares, it was decided to cut it and fit the pieces together to form a board,

blacking some of the squares afterwards for convenience in playing.

An ingenious Scotsman showed how this could be done by cutting the stuff in two pieces only,

and it is a really good puzzle to discover how he did it.

Cut the linoleum along the lines into two pieces that will fit together and form the board, eight by eight.

$119$ - 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?