Set 04

Wooden Disc

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Here is a wooden disc, about an inch thick, that has been sitting for over a hundred years on the counter in a little country store in Vermont. The circumference of the disc is exactly 27 in. (the diameter is a little less than 9 in.). There are six wooden pegs sticking out of the edge of the disc; two of them are shown. The disc is used to measure lengths of ribbon. The pegs are arranged so that any unit length of ribbon, from 1 to 27 inches, can be measured simply by laying off the ribbon along the edge of the disc between some pair of nails or other. Where can you put the other four pegs so that this is possible?

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Poison Pills

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These funnels were devised by an ancient king to determine which of his captives should die. They contained white sugar pills and black poison pills. Each funnel had a spring release at the end to let one pill fall at a time when the spring was pressed at point A on Fig. 1, which shows a black pill about to fall.

Each captive’s fate depended on the second pill that fell into his hand. He had to replace the first pill in the funnel, no matter what its color, and swallow the second one.

Referring to the picture and description, see if you can answer these questions:

Fig. 1 shows 12 pills ready to be drawn by 9 captives. Captive #1 draws the black pill first, replaces it at the top, and eats pill #2. Then captive #2 draws pill #3, replaces it at the top, and eats pill #4. Which of the 9 captives has to eat one of the black poison pills?

Fig. 2 shows no poison pills. Again supposing that there were 9 captives, where would you put 3 black pills so that none would be drawn as a second choice? Show your solution by blacking in three of the pills.

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Knots

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See if you can unravel these six pieces of rope without getting caught in the loops. Grasp the two ends firmly in your mind, then imagine yourself pulling them until you have a straight piece of rope – either with a knot or without one. In certain cases these figures form knots; in others they just form loops that pull right out. Find the knots and mark your choices by underlining the letters below the figures you think will become knotted.

     
     


     
     

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