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# Crossing the Bridge Puzzle

## Crossing the Bridge

In Crossing the Bridge Puzzle, a bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a dark night and there is only one torch between them. Only two people can cross at a time. “A” takes a minute to cross. “B” takes 2 minutes, “C” takes 5 minutes and “D” takes 10 minutes. How do they all cross before the bridge cross ?

## Crossing the Bridge

In Crossing the Bridge Puzzle, a bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a dark night and there is only one torch between them. Only two people can cross at a time. “A” takes a minute to cross. “B” takes 2 minutes, “C” takes 5 minutes and “D” takes 10 minutes. How do they all cross before the bridge cross ?

## Solution

Here we have provided information for solution of Crossing the Bridge Puzzle :

Time in which bridge will collapse = 17 mins

Number of people wants to cross the bridge = 4 people

Number of torch they have = 1

Time take by A to cross the bridge = 1 minute

Time taken by B to cross the bridge = 2 minutes

Time taken by C to cross the bridge = 5 minutes

Time taken by D to cross the bridge = 10 minutes

```
Move Time
A & B Cross with torch 2 min
A return with torch 1 min
C & D Cross with torch 10 min
B return with torch 2 min
A & B cross with torch 2 min
```

Total time 17 min

## Detail Analysis

A & B crosses the bridge in 2 mins and returns with the torch in 1 mins, so total time taken by now is 3 min.

**Time left before the bridge collapse = 14 mins**

C & D crosses the bridge in 10 mins and B returns with the torch in 2 mins, so total time taken by now is 15 min.

**Time left before the bridge collapse = 2mins**

Now, A & B were only left out and time left before the bridge collapse in 2 min but the maximum time taken by A & B to cross the bridge is 2 mins as time taken by A is 1 min and by B is 2 mins.

**Hence A, B, C and D all four will cross the bridge within 17 mins.**

## Solution

Here we have provided information for solution of Crossing the Bridge Puzzle :

Time in which bridge will collapse = 17 mins

Number of people wants to cross the bridge = 4 people

Number of torch they have = 1

Time take by A to cross the bridge = 1 minute

Time taken by B to cross the bridge = 2 minutes

Time taken by C to cross the bridge = 5 minutes

Time taken by D to cross the bridge = 10 minutes

```
Move Time
A & B Cross with torch 2 min
A return with torch 1 min
C & D Cross with torch 10 min
B return with torch 2 min
A & B cross with torch 2 min
```

Total time 17 min

## Detail Analysis

A & B crosses the bridge in 2 mins and returns with the torch in 1 mins, so total time taken by now is 3 min.

**Time left before the bridge collapse = 14 mins**

C & D crosses the bridge in 10 mins and B returns with the torch in 2 mins, so total time taken by now is 15 min.

**Time left before the bridge collapse = 2mins**

Now, A & B were only left out and time left before the bridge collapse in 2 min but the maximum time taken by A & B to cross the bridge is 2 mins as time taken by A is 1 min and by B is 2 mins.

**Hence A, B, C and D all four will cross the bridge within 17 mins.**

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