The Logical Puzzle - 24 Jan 2007

The Logical Puzzle - 24 Jan 2007

Solution to January's Puzzle: Crossing the Tunnel

Four people—let's call them persons A, B, C, and D—need to cross a dark tunnel. Only two people at a time can cross the tunnel, and because the tunnel is very dark, a flashlight is mandatory. Person A can cross the tunnel in 1 minute, person B can cross in 2 minutes, person C can cross in 4 minutes, and person D can make it in 5 minutes. The group has one flashlight, containing batteries that last only 12 minutes. What strategy will enable all members of the group to cross to the other side in 12 minutes before the flashlight's batteries run down?

Most people try to solve this puzzle by letting person A walk from start to end with each of the others, then walk back alone to pair with the next person. Intuition says that this approach must be the fastest because person A is the fastest. But if you calculate the total time it takes all four people to get to the end, you get 13 minutes. Of course, the pace is dictated by the slowest in the pair. Person A would need to go from start to end three times: with B (2 minutes), C (4 minutes), and D (5 minutes). These walks amount to 11 minutes, plus add two times that person A needs to walk back alone (1 minute per walk), and you get 13. The trick in solving the puzzle is to figure out that you can save most time by letting the two slowest people walk together. Here's the strategy that gets all the people across in 12 minutes:

  • Persons A and B walk first from start to end (2 minutes)
  • Person A walks back (1 minute)
  • Persons C and D walk from start to end (5 minutes)
  • Person B walks back (2 minutes)
  • Persons A and B walk from start to end (2 minutes)

February's Puzzle: Escaping a Cave

While hiking a mountain, you enter a cave. Suddenly, rocks fall and block the cave's entrance. You turn on your flashlight and start walking deeper into the cave. After a while, you find another opening. Unfortunately, however, the opening gives way to a sheer rock wall 60 feet above a hikeable surface. You figure that 10 feet is the most distance you could jump down without sustaining serious injuries (also taking your own height into consideration).

You look around the cave and find that the ceiling is very high—40 feet above the floor. After a while, you find a 40-foot rope hanging from ceiling to floor. A few minutes later, you find another 40-foot rope hanging from ceiling to floor. You have your hiking knife with you. Can you think of a plan that will let you get out of the cave and down the hikeable surface without jumping down more than 10 feet?

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