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?

for convenience designate each person by the time it takes them to cross

time | Action
00 | 20,43 and 37,41 set out
41 | 37, 41 arrive
43 | 20,43 arrive 20 returns w/ both lights
63 | 20 arrives w/lights 20,34 and 29,31 set out
94 | 29,31 arrive
97 | 20,34 arrive; 20 returns w/both lights
117 | 20 arrives w/lights 20,27 and 21,23 set out
140 | 21,23 arrive
144 | 20,27 arrive, all are across

Posted by Andrew Mitchell on 2003-07-28 09:00:32