perplexus.info :: General : Ten at a Bridge

Ten at a Bridge (Posted on 2003-07-28)

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?

Submitted by Brian Smith

Rating: 3.4286 (7 votes)

Solution: (Hide)

At T=0: Flashlight 1 is carried to the finish by #20 and #21 Flashlight 2 is carried to the finish by #23 and #43
At T=21: Flashlight 1 is carried to the start by #21
At T=42: Flashlight 1 is carried to the finish by #37 and #40
At T=43: Flashlight 2 is carried to the start by #20
At T=63: Flashlight 2 is carried to the finish by #20 and #21
At T=82: Flashlight 1 is carried to the start by #23
At T=84: Flashlight 2 is carried to the start by #20
At T=104: Flashlight 2 is carried to the finish by #31 and #34
At T=105: Flashlight 1 is carried to the finish by #20 and #23
At T=128: Flashlight 1 is carried to the start by #21
At T=138: Flashlight 2 is carried to the start by #20
At T=149: Flashlight 1 is carried to the finish by #27 and #29
At T=158: Flashlight 2 is carried to the finish by #20 and #21
At T=178: Flashlight 1 arrives at the finish
At T=179: Flashlight 2 arrives at the finish
All members are across in 179 minutes.
Note: Our members have submitted a number of more optimal solutions in the comments (fwaff's allows everyone to cross in 142 minutes)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: SOLN	Viet	2003-07-28 09:41:34
Solution	Andrew Mitchell	2003-07-28 09:00:32
re: SOLN	fwaff	2003-07-28 08:05:48
SOLN	suyarajan	2003-07-28 04:18:21
re: Solution	Trevor Leitch	2003-07-28 03:29:35
Solution	Lewis	2003-07-28 02:03:22

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