four person can cross a bridgeBlog

four person can cross a bridge

First, we show that if the two slowest persons (C and D) cross separately, they accumulate a total crossing time of 15.

When Assume that a solution minimizes the total number of crossings. Four people come to a river in the night. Problem is that it’s dark and so you can’t cross the bridge without a flashlight and they only have one flashlight. To make matters worse, it is night-time and there is only one torch.

\n3rd. Several variations exist, with cosmetic variations such as differently named people, or variation in the crossing times or time limit.The puzzle is known to have appeared as early as 1981, in the book In the case where there are an arbitrary number of people with arbitrary crossing times, and the capacity of the bridge remains equal to two people, the problem has been completely analyzed by Martin Erwig from Oregon State University has used a variation of the problem to argue for the usability of the Haskell programming language over Prolog for solving The puzzle is also mentioned in Daniel Dennett's book But then C or D must cross back to bring the torch to the other side, and so whoever solo-crossed must cross again.

But then C or D must cross back to bring the torch to the other side, and so whoever solo-crossed must cross again.

Four friends A, B, C, D Need to cross a bridge.. A maximum of 2 people can cross at a time.. People that cross the bridge must carry the lamp to see the way.. The flashlight can only travel with a person so every time it crosses the bridge it … There is a narrow bridge, but it can only hold two people at a time. To cross the bridge, the time taken by them is as follows: A: 1 minute, B: 2 minutes, C: 7 minutes and D: 10 minutes. The people have one flashlight, which needs to be held by any group crossing the bridge because of how dark it is.

(Here we use A because we know that using A to cross both C and D separately is the most efficient.) The bridge is rickety and can only support 2 people at a time. Person A can cross the bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 8 minutes. The puzzle is Four people need to cross a rickety bridge at night.

The bridge can only hold two or less people at any time and they only have one flashlight so they must travel together (or alone). Then, A must cross next, since we assume we should choose the fastest to make the solo-cross. Also, it is impossible for them to cross together last, since this implies that one of them must have crossed previously, otherwise there would be three persons total on the start side. Finally, the lamp has to be returned at the original place and the person who returns the lamp has to cross the bridge again without a lamp. This strategy makes A the torch bearer, shuttling each person across the bridge:This strategy does not permit a crossing in 15 minutes.

This is a popular question asked and answered about 4-5 years back.

This gives us, B+A+D+B+B = 2+1+8+2+2 = 15. Putting all this together, A and B must cross first, since we know C and D cannot and we are minimizing crossings. \n2nd. Then, A must cross next, since we assume we should choose the fastest to make the solo-cross. Assume that C and D cross first. It is night and they have just 1 lamp. Plus the bridge is only big enough for two people to cross at once. This gives a total of five crossings - three pair crossings and two solo-crossings. Four friends A, B, C and D need to cross a bridge. Remember our assumption at the beginning states that we should minimize crossings and so we have five crossings - 3 pair-crossings and 2 single crossings. Then we choose to send the fastest back, which is B.

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