# Al the Chemist II

This is the second part of the problem from Raymond Smullyan in the “Brain Bogglers” section of the 1996 Discover magazine.

“On another occasion, Al made a mixture of water and wine. There was more water than wine—in fact, the excess of water over wine was equal to one-fourth the quantity of wine. Al then added 12 ounces of wine, at which point there was one ounce more of wine than water.

According to another version of the story, before Al added the 12 ounces of wine, he first boiled off 12 ounces of water (the net effect being that he replaced 12 ounces of water with wine), and again there was one more ounce of wine than water.

Would there be more mixture present at the end of the first version or the second?”

I found this statement a tad ambiguous with the result that I found two possible solutions: the one Smullyan gave and another, surprising one.

# Al the Chemist I

This is a relatively simple problem from the inventive Raymond Smullyan in the “Brain Bogglers” section of the 1996 Discover magazine.

“AL THE CHEMIST—not an alchemist, though his name might suggest it­—one day partially filled a container with some concoction or other. He knew the volume of fluid in the container, as well as the volume of empty space, and real­ized that two-thirds of the former was equal to four-fifths of the latter. Was the container then less than half full, more than half full, or exactly half full?”

See Al the Chemist I for solution.

# 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  for solutions.