Cardboard Chain
Answer :

We will suppose that he has a piece of cardboard measuring 8 in. by 2½ in., though the dimensions are of no importance. 
Yet if you want a long chain you must, of course, take a long strip of cardboard. 
First rule pencil lines B B and C C, half an inch from the edges, and also the short perpendicular lines half an inch apart. 
Rule lines on the other side in just the same way, and in order that they shall coincide it is well to prick through the card with a needle the points where the short lines end. 
Now take your penknife and split the card from A A down to B B, and from D D up to C C. 
Then cut right through the card along all the short perpendicular lines, and half through the card along the short portions of B B and C C that are not dotted. 
Next turn the card over and cut half through along the short lines on B B and C C at the places that are immediately beneath the dotted lines on the upper side. 
With a little careful separation of the parts with the penknife, the cardboard may now be divided into two interlacing ladder-like portions, as shown in Fig. 2; and if you cut away all the shaded parts you will get the chain, cut solidly out of the cardboard, without any join, as shown in the illustrations on page 40.

It is an interesting variant of the puzzle to cut out two keys on a ring—in the same manner without join.

Math Genius