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This is a pretty cool and interesting question from AMC. There are four lifts in a building. Each makes three stops, which do not have to be on consecutive floors on include the ground floor. For [...]

The positive integers and satisfy What is the value of ?

All possible straight lines joining the vertices of a cube with mid-points of its edges are drawn. At how many points inside the cube do two or more of these lines meet?

A student asked me this question recently. I think this is from AMC. There are 42 points placed on a straight line so that each distance from to is where . What is the sum of the distances [...]