There are two magic time boxes. One box makes the time in it sqrt(2) times as fast as the time out of it. The other box makes the time in it sqrt(3) times as fast as the time out of it. You have two straight sticks, each is 1 meter long, and have two ants, they move at same speed. (Be aware, an ant seems faster when it is in a box.) The boxes are transparent, and you can make accurate comparison on distance which ants have moved between sticks even in different boxes. How to find 1/3 meter length? How to find 1/5 meter length?
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There is no limitation on boxes’ size (you can enter a box if you want). You can mark the sticks. You are not allow to break them. You can do anything reasonable, for example: put a part of stick in one box, and put the rest of it in the other box.