175—­ANOTHER PATCHWORK PUZZLE.

[Illustration]

A lady was presented, by two of her girl friends, with the pretty pieces of silk patchwork shown in our illustration.  It will be seen that both pieces are made up of squares all of the same size—­one 12 x 12 and the other 5 x 5.  She proposes to join them together and make one square patchwork quilt, 13 x 13, but, of course, she will not cut any of the material—­merely cut the stitches where necessary and join together again.  What perplexes her is this.  A friend assures her that there need be no more than four pieces in all to join up for the new quilt.  Could you show her how this little needlework puzzle is to be solved in so few pieces?

176.—­LINOLEUM CUTTING.

[Illustration]

The diagram herewith represents two separate pieces of linoleum.  The chequered pattern is not repeated at the back, so that the pieces cannot be turned over.  The puzzle is to cut the two squares into four pieces so that they shall fit together and form one perfect square 10 x 10, so that the pattern shall properly match, and so that the larger piece shall have as small a portion as possible cut from it.

177.—­ANOTHER LINOLEUM PUZZLE.

[Illustration]

Can you cut this piece of linoleum into four pieces that will fit together and form a perfect square?  Of course the cuts may only be made along the lines.

VARIOUS GEOMETRICAL PUZZLES.

    “So various are the tastes of men.” 
        MARK AKENSIDE.

178.—­THE CARDBOARD BOX.

This puzzle is not difficult, but it will be found entertaining to discover the simple rule for its solution.  I have a rectangular cardboard box.  The top has an area of 120 square inches, the side 96 square inches, and the end 80 square inches.  What are the exact dimensions of the box?

179.—­STEALING THE BELL-ROPES.

Two men broke into a church tower one night to steal the bell-ropes.  The two ropes passed through holes in the wooden ceiling high above them, and they lost no time in climbing to the top.  Then one man drew his knife and cut the rope above his head, in consequence of which he fell to the floor and was badly injured.  His fellow-thief called out that it served him right for being such a fool.  He said that he should have done as he was doing, upon which he cut the rope below the place at which he held on.  Then, to his dismay, he found that he was in no better plight, for, after hanging on as long as his strength lasted, he was compelled to let go and fall beside his comrade.  Here they were both found the next morning with their limbs broken.  How far did they fall?  One of the ropes when they found it was just touching the floor, and when you pulled the end to the wall, keeping the rope taut, it touched a point just three inches above the floor, and the wall was four feet from the rope when it hung at rest.  How long was the rope from floor to ceiling?