# Torch and Bridge - Bridge Crossing Puzzle || Logical Interview Puzzle

Interview logical puzzles are a type of problem or challenge that is designed to test a person's critical thinking, problem-solving, and reasoning skills. These puzzles are commonly used in job interviews for positions that require analytical and problem-solving abilities, such as software development, data analysis, and management roles.

Puzzle Details :

There are 4 persons (A, B, C, and D) who want to cross a bridge at night.

• A takes 1 minute to cross the bridge.
• B takes 2 minutes to cross the bridge.
• C takes 5 minutes to cross the bridge.
• D takes 8 minutes to cross the bridge.

There is only one torch with them and the bridge cannot be crossed without the torch. There cannot be more than two persons on the bridge at any time, and when two people cross the bridge together, they must move at the slower person’s pace. Can they all cross the bridge in 15 minutes?

Solution

The initial solution, most people will think of, is to use the fastest person a guide everyone across. In this case,  it will take 8 + 1 + 5 + 1 + 2 = 17 mins. to cross the bridge, which is incorrect.

Let’s brainstorm a little further, To reduce the amount of time. let's check now how that can be achieved.

first step,

1 and 2 cross the bridge. here the number represents the time taken by the corresponding person to cross the bridge. 1 comes back. total Time taken is 3 minutes. Now 2 is on the other side.

Second step

5 and 8 cross the bridge. 2 comes back. Time taken will 8 + 2 minutes that is 10 minutes. Now 5 and 8 are on the other side.

Third Step

1 and 2 cross the bridge. and Time taken is 2 minutes. now All are on the other side. Total time spent is 3 + 10 + 2 = 15 minutes.

15 minutes is the shortest time needed for all four of them to cross the bridge.

Watch the below video for a detailed explanation.