Once there four boys who wanted to cross a street. They were all on the same side. It was night time and they only had one flashlight between them. Only two boys can cross the street at a time, and anyone who crosses , either one or two people, must always have a flashlight with them. For his work, the flashlight must be walked back and forth. It cannot be thrown or forgotten. Another issue is that each boy walks at a different speed. A pair must walk together al the speed of the slower boy. Listed below is the amount of time each boy needs to cross the street:

Boy # 1needs 1 minute
Boy # 2 needs 2 minute
Boy #3 needs 5 minute
Boy # 4 needs 10 minutes

How can all four boys cross the street in 17 minutes ?

To ensure all four boys can cross the street in 17 minutes, follow these steps:

1. Boy #1 and Boy #2 cross the street together, taking 2 minutes. (Total time: 2 minutes)

2. Boy #1 takes the flashlight back, requiring 1 minute. (Total time: 3 minutes)

3. Boy #3 and Boy #4 cross the street together, taking 10 minutes. (Total time: 13 minutes)

4. Boy #2 takes the flashlight back, requiring 2 minutes. (Total time: 15 minutes)

5. Finally, Boy #1 and Boy #2 cross the street together again, taking 2 minutes. (Total time: 17 minutes)

By following this sequence, all four boys can successfully cross the street in 17 minutes.

To figure out how all four boys can cross the street in 17 minutes, we need to find a combination of pairs that will take the least amount of time.

First, we should identify the two slowest boys since they will determine the overall time taken. In this case, Boy #3 (5 minutes) and Boy #4 (10 minutes) are the slowest.

To minimize the time taken, we should pair the slowest boy, Boy #4, with the fastest boy, Boy #1. They will take 10 minutes to cross the street.

Next, Boy #1 should go back with the flashlight, which will take 1 additional minute.

Now, we need to pair Boy #3 (5 minutes) with one of the remaining boys - Boy #2 (2 minutes) or Boy #3 (5 minutes). If we pair them, it will take 5 minutes to cross the street.

In this case, let's pair Boy #3 and Boy #2. They will take 2 minutes to cross the street.

Again, Boy #1 should go back with the flashlight, taking another 1 minute.

Now, we have Boy #1 (1 minute) and Boy #2 (2 minutes) left on the original side of the street.

To minimize the time, pair them together, and they will take 2 minutes to cross the street.

By following this strategy, all four boys can cross the street in a total of 10 + 1 + 5 + 1 + 2 = 19 minutes.

However, this solution takes longer than the desired 17 minutes. Let's re-analyze the situation.

If we pair Boy #3 (5 minutes) with Boy #4 (10 minutes), they will take 10 minutes to cross, as before. But this time, instead of coming back alone, Boy #3 can take the flashlight and return, which will take 5 minutes.

Meanwhile, Boy #1 (1 minute) and Boy #2 (2 minutes) can cross the street together, taking 2 minutes. Boy #2 should then take the flashlight and return alone, requiring an additional 2 minutes.

Finally, Boy #1 (1 minute) and Boy #2 (2 minutes) can cross the street together again in 2 minutes.

By using this revised strategy, all four boys can cross the street in a total of 10 + 5 + 2 + 2 + 2 = 21 minutes.

Unfortunately, we still haven't reached the desired 17 minutes. Let's adjust the approach once more.

This time, let's pair Boy #1 (1 minute) with Boy #2 (2 minutes) to cross the street. It will take 2 minutes.

Boy #1 should bring the flashlight back, which will take 1 minute.

Next, we will pair Boy #3 (5 minutes) with Boy #4 (10 minutes) to cross the street. They will take 10 minutes.

Boy #2 (2 minutes) should bring the flashlight back, which will take 2 minutes.

Finally, Boy #1 (1 minute) and Boy #2 (2 minutes) can cross the street together, taking 2 minutes.

By following this adjusted strategy, all four boys can cross the street in a total of 2 + 1 + 10 + 2 + 2 = 17 minutes.

Therefore, by pairing the boys strategically and assigning different roles for each crossing, it is possible for all four boys to cross the street in precisely 17 minutes.