# Family Values

Here is a collection of puzzles from the great logic puzzle master Raymond Smullyan in a “Brain Bogglers” column for the 1996 Discover magazine.

1. ELDON WHITE HAS FOUR DOGS. One day he put out a bowl of dog biscuits. The eldest dog came first and ate half the biscuits plus one more. Then the next dog came and ate half of what he found plus one more. Then the next one came and ate half of what she found plus one more. Then the little one came and ate half of what she found and one more, and that finished the biscuits. How many biscuits were originally in the bowl?
2. Eldon once bought a very remarkable plant, which, on the first day, increased its height by a half, on the second day by a third, on the third day by a quarter, and so on. How many days did it take to grow to 100 times its original height?
3. In addition to four dogs, Eldon has four children. The youngest, Betty, is nine years old; then there are twin boys, Arthur and Robert; and finally there’s Laura, the eldest, whose age is equal to the combined ages of Betty and Arthur. Also, the combined ages of the twins are the same as the combined ages of the youngest and the eldest. How old is each child?
4. “How about a riddle?” asked Robert. “Very well,” said Eldon. “What is it that is larger than the universe, the dead eat it, and if the living eat it, they die?”

See Family Values.

Here is another Brain Bogglers problem from 1987 by Michael Stueben.

“A quadrilateral with sides three, two, and four units in length is inscribed in a circle of diameter five.  What’s the length of the fourth side of the quadrilateral?”

Like a number of other Brain Bogglers this problem also uses an insight that makes the solution easy.

See the Quad in Circle Problem.

# Factory Location Problem

This is a somewhat elegant problem from the 1987 Discover magazine’s Brain Bogglers by Michael Stueben:

“Each dot in the figure at left represents a factory. On which of the city’s 63 intersections should a warehouse be built to make the total distance between it and all the factors as short as possible? (A much simpler solution than counting and totaling the distances is available.)”

Note that the distance is the taxicab distance I discussed in my article South Dakota Travel Problem rather than the distance along straight lines between the warehouse and factories.

See the Factory Location Problem

# Movie Projector Problem

Here is another Brain Bogglers problem from 1987.

“Exactly four minutes after starting to run—when the take-up reel was rotating one and a half times as fast as the projecting reel—the film broke. (The hub diameter of the smaller take-up reel is 8 cm and the hub diameter of the projecting reel is 12 cm.) How many minutes of film remain to be shown?”

This feels like another problem where there is insufficient information to solve it, and that makes it fun and challenging. In fact, I was stumped for a while until I noticed something that was the key to completing the solution.

See the Movie Projector Problem.

# 1770 Card Game Problem

This problem from the 1987 Discover magazine’s Brain Bogglers by Michael Stueben apparently traces back to 1770, though the exact reference is not given.

“Here’s an arithmetic problem taken from a textbook published in Germany in 1770. Three people are gambling. In the first game, Player A loses to each of the others as much money as each of them had when the game started. In the next game, B loses to each of the others as much money as each had when that game began. In the third game, A and B each win from C as much money as each had at the start of that game. The players now find that each has the same sum, 24 guineas. How much money did each have when play began?”

See the 1770 Card Game Problem