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Burning ropes
You have two ropes, each of which takes 1 hour to burn. But either rope has different
densities at different points, so there's no guarantee of consistency in the time it takes
different sections within the rope to burn. How do you use these two ropes to measure 45
minutes?
Horse race
There are 25 horses, each of which runs at a constant speed that is different from the
other horses’. Since the track only has 5 lanes, each race can have at most 5 horses. If
you need to find the 3 fastest horses, what is the minimum number of races needed to
identify them?
River crossing
Four people, A, B, C and D need to get across a river. The only way to cross the river is
by an old bridge, which holds at most 2 people at a time. Being dark, they can't cross the
bridge without a torch, of which they only have one. So each pair can only walk at the
speed of the slower person. They need to get all of them across to the other side as
quickly as possible. A is the slowest and takes 10 minutes to cross; B takes 5 minutes; C
takes 2 minutes; and D takes 1 minute.
What is the minimum time to get all of them across to the other side? |
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