## Least time

There are 4 women who want to cross a bridge.

They all begin from the same side. It is night. There is one flashlight.

A maximum of two people can cross at a time.

Any one, who crosses (either 1 or 2 persons), must have the flashlight with them.

The flashlight must be taken back and forth.

Each woman walks at a different speed.

A pair must walk together at the pace of the slower woman.

Woman 1 : Takes 1 minute to cross

Woman 2 : Takes 2 minutes to cross

Woman 3 : Takes 5 minutes to cross

Woman 4: Takes 10 minutes to cross

For example if Woman 1 and Woman 4 walk together first, 10 minutes will elapse when they get to the other side of the bridge.

All women have to across the bridge in the least time.

Please help them.

17min

let us assume women 1 is having flash light. then W1 and W4 take 10 min, W1and W3 take 5min, W1 and W2 take 2min…

So 10+5+2=17

your analysis is wrong. If w1 and w4 take the first trip, for the second trip , w1 should come back , it will take another minute.