Thread: Logical solution

There are 4 people who need to cross the bridge at night .the bridge is only wide enough for two people to cross at once.there is only one flashlight for the entire group .when two people cross they must cross at the slower member's speed.all 4 people must cross the bridge in 17 minutes since the bridge will collapse in exactly that amount of time

person1:1 minute

person2: 2 minutes

person 3: 5 minutes

person 4: 10 minutes

for example if person 1 and person 4 walk across first 10 minutes have elasped when they got to the other side of the bridge.if person 4 returns the flashlight a total of 20 minutes have passed and you have failed the mission

how to logically construct this equation

Does it have to be the case that every time the bridge is crossed, the flashlight must be held by one of those crossing the bridge at the time?

the trick is, we want to send number 3 and number 4 across at the same time (this saves us 5 minutes, because the 10 minutes guy is the slowest).

however, we do NOT want to send the 5 minute guy back across the bridge (or else we use at LEAST 20 minutes up getting him back).

so somebody fast must already be waiting there to carry the flashlight back. what is the fastest way to get the flashlight and the fastest guy across the bridge, and leave him there, bringing the flashlight back?