Train Your Brain

Many people start the day with physical exercise, but fewer of us seem concerned with giving our brains a daily workout. Train Your Brain aims to reverse this unfortunate trend with a perplexing array of mathematical recreations organized into 52 sections that are labeled weeks 1 through 52—enough to keep your brain cells crackling all year round.

Dip into these pages and you’ll encounter puzzles such as:
• Twice a day, at noon and midnight Universal Time, a ship leaves New York for Lisbon, and another leaves Lisbon for New York. The ships travel the same route, and passage takes exactly eight days. Recently, I traveled on one of these ships from New York to Lisbon. How many passing ships did I count? (Include those arriving at my departure and those departing on my arrival.)
• A brass rod weighs 85 lb. I want to saw it into two pieces, so that the weight of each piece is a (whole) multiple of 1 lb. In how many ways can I do this?
• In a math class, the students are designing flags. Each flag is divided into three parts by two vertical lines. The children color the three stripes with red, blue, green or yellow. How many flags are possible if a color can be used only once on each flag?
• Two jealous husbands wish to cross a river with their wives, but there is only one two-person boat available. Neither of the two men wants to leave his wife alone with the other man. How can they manage the crossing?
• “It’s interesting,” says Susie, “that my mother is exactly half as old as my father and I put together. Between them, my father and my mother are 100 years old, and the age of each is a prime number.” How old is Susie? (answers below.)

Complete with hints and solutions to each puzzle, Train Your Brain provides a healthy dose of intellectual calisthenics.


Answers to questions above:
• 33 ships.
• 84 ways.
• 24 flags.
• One couple crosses the river, the husband returns, the men cross, the second husband returns, the second couple crosses.
• Susie is 23.

Answers to illustration questions:
• Can you explain how this addition problem is correct? (Answer: The problem is written in base 9.)
• Is it possible to tour this garden so that each path is traversed only once? If so, which staircase should a visitor use? (Answer: Yes, and either staircase 2 or 3 works.)