I cut the two squares in the manner desired into four pieces that would fit together and form another larger square, taking care that the pattern should match properly, and when I had finished I noticed that two of the pieces were of exactly the same area; that is, each of the two contained the same number of chequers. Can you show how the cuts were made in accordance with these conditions? 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.