Friday, March 4, 2011

The Rickety Bridge

Andrew, Beth, Carol and Daniel are on vacation and have spent the day exploring the mountain ranges in Yellowstone National Park. Having lost track of time, darkness is setting in and they are in a hurry to get back. But then there is a rickety old wooden bridge on their path, suspended high over a deep ravine. There's a warning-sign stating that the bridge will only be able to carry the weight of two persons at a time.

No-one is willing to cross the dangerous bridge without the light of a flashlight... unfortunately the group only has one of those with them. They can't risk throwing it, thus it needs to be carried back and forth.

Because of their different ages and fitness levels they will all cross at different speeds. Andrew can cross in 1 minute, Beth in 2 minutes, Carol in 4 minutes and Daniel in 5 minutes. For each duo, the slowest will of course determine the duration of crossing.

Soon it will be night and pitch black. Therefore the group wants to cross the bridge in the minimum time possible. Andrew thinks for a moment and then announces it can be done in 12 minutes. No trick. How?

Your initial thought may be to get Andrew to accompany the others to the other side. One at a time, returning each time to accompany the next one. After all, he is the fastest, so his way back will waste the least amount of time out of all four of them. But this yields 2 + 1 + 4 + 1 + 5 = 13 minutes! There must be a faster way.

The key is to let the two slowest persons cross at the same time, without either returning. Here it is.
  • First Andrew and Beth will cross. (2 min.)
  • Andrew returns with the flashlight. (1 min.)
  • Carol and Daniel take the flashlight and cross. (5 min.)
  • Beth is still waiting there, so she takes the flashlight and returns. (2 min.)
  • She can now cross together with Andrew. (2 min.)
That's a total of 12 minutes. They made it!

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