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You have two ropes. Each rope takes one hour to burn. These ropes are not identical, nor are they uniform; i.e. it does not necessarily take half an hour for half the rope to burn (if you have trouble visualizing this, imagine a rope of varying thickness across its length). With only these two ropes and a way to light them, how do you measure out 45 minutes?
Light both ends of one rope, and only one end of the other rope. This will cause the first rope to burn out in 30 minutes. When the first rope burns out, there will be 30 minutes left on the second rope. So then, light the other end of the second rope, and the rest of it will burn out in 15 minutes. 30 + 15 = 45 minutes.