Four people need to cross a bridge at night which only supports two people at the same time. They have one torch and the bridge is too risky to cross without the torch. They all walk at different speeds, one can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes and the last takes 10 minutes to cross. When two people cross the bridge together, they must walk at the slower person’s pace. What is the least amount of time in which all people can cross the bridge?

Let’s label the people A, B, C, and D, where A takes 1 minute, B takes 2 minutes, C takes 5 minutes, and D takes 10 minutes to cross the bridge.

We want to minimize the total time taken for all four people to cross the bridge. We can discuss a strategy where the faster people (A and B) help to shuttle the slower people (C and D) across the bridge, minimizing the number of times the slower people need to cross.

Here’s the step-by-step strategy:

1. A and B cross the bridge together. The time taken is 2 minutes (B’s speed).

2. A goes back with the torch. The time taken is 1 additional minute.

3. C and D cross the bridge together. The time taken is 10 minutes (D’s speed).

4. B goes back with the torch. The time taken is 2 additional minutes.

5. A and B cross the bridge together again. The time taken is 2 additional minutes.

Now, all people have crossed the bridge. The total time taken can be calculated as follows:

Total Time = 2 + 1 + 10 + 2 + 2 = 17 minutes.

So, the least amount of time in which all people can cross the bridge is 17 minutes.