There’s a family of 4 people, and they’re fleeing to safety across a rickety bridge that’s swept away by a flood in 17 minutes. The family members have 1 flashlight, which they must use every time they cross the bridge. The Grandfather will take 10 minutes to cross the bridge, the mother 5 minutes, the brother 2 mintues, and the sister 1 minute. No more than 2 family members can be on the bridge at any one given time? Do they make it? If so, is there more than one way for them to make it across?
_This problem was something that Andrew (whom I tutor) was assigned as part of a problem of the week._
h4. Solution
# brother + sister cross: 2 min.
# sister returns w/flashlight: 1 min
# grandpa + mother cross: 10 min
# brother returns w/flashlight: 2 min
# brother + sister cross: 2 min
*Total time: 17 min*
h4. Alt. Solution
# brother + sister cross: 2 min.
# brother returns w/flashlight: 2 min
# grandpa + mother cross: 10 min
# sister returns w/flashlight: 1 min
# brother + sister cross: 2 min
*Total time: 17 min*
h4. Strategy
Since the time it takes on each journey is determined by the slowest person crossing on that journey, *the best way to speed up the overall crossing is to have the 2 slowest people cross together.* If Grandpa and Grandma cross together, then it takes a total of 10 minutes vs. 15 minutes if they had crossed seperately. Brother and Sister have to cross first so that someone fast is on the other side to bring the flashlight back. It doesn’t matter which of them brings the flashlight back the first time (hence the 2 solutions) because they will both end up making a total of 3 trips.
Bridge Crossing Problem
Tags: it · problem
There’s a family of 4 people, and they’re fleeing to safety across a rickety bridge that’s swept away by a flood in 17 minutes. The family members have 1 flashlight, which they must use every time they cross the bridge. The Grandfather will take 10 minutes to cross the bridge, the mother 5 minutes, the brother 2 mintues, and the sister 1 minute. No more than 2 family members can be on the bridge at any one given time? Do they make it? If so, is there more than one way for them to make it across?
_This problem was something that Andrew (whom I tutor) was assigned as part of a problem of the week._
h4. Solution
# brother + sister cross: 2 min.
# sister returns w/flashlight: 1 min
# grandpa + mother cross: 10 min
# brother returns w/flashlight: 2 min
# brother + sister cross: 2 min
*Total time: 17 min*
h4. Alt. Solution
# brother + sister cross: 2 min.
# brother returns w/flashlight: 2 min
# grandpa + mother cross: 10 min
# sister returns w/flashlight: 1 min
# brother + sister cross: 2 min
*Total time: 17 min*
h4. Strategy
Since the time it takes on each journey is determined by the slowest person crossing on that journey, *the best way to speed up the overall crossing is to have the 2 slowest people cross together.* If Grandpa and Grandma cross together, then it takes a total of 10 minutes vs. 15 minutes if they had crossed seperately. Brother and Sister have to cross first so that someone fast is on the other side to bring the flashlight back. It doesn’t matter which of them brings the flashlight back the first time (hence the 2 solutions) because they will both end up making a total of 3 trips.