Ten people on a war games weekend come to a railroad bridge. It is midnight and there is no moon. Crossing is very dangerous because the ties are slippery and unevenly spaced.

The people are of differing ages and fitness. The times it takes each person to cross individually are 20, 21, 23, 27, 29, 31, 34, 37, 41, and 43 minutes respectively. Each person knows everyone's time.

They have just 2 small flashlights, and each one casts only enough light to allow two people to cross safely. Whenever 2 people cross together, they cross in the time of the slower person.

The flashlights can be handed off at either end, but not part way. Crossers never turn around or stop on the bridge.

Everyone can get across in 3 hours (180 minutes) or less. How is this accomplished?

(In reply to SOLN by suyarajan)

Almost - you've sent 27 across twice and forgotten about 31. Revising your solution gives:

*Send 20, 21, 23 and 27 across with both lights. Send 20 back with both lights for a total time of 47 minutes.

* Send 43,41,37, and 34 across with both lights. Send 21 back with both lights for a total time of 111 minutes.

* Now just send 20, 21, 29 and 31 across with both lights. Everybody is across in only 142 minutes.

Posted by fwaff on 2003-07-28 08:05:48