Math CentralQuandaries & Queries


Question from Travis, a student:

If you are sitting on chair 33 of a ski lift, which is a loop.
Chairs are numbered consecutively, starting with 1.
Chair 97 passes you halfway up the ski slope.
How many chairs are on the lift?

Can you show the answer in a diagram or sketch, graph, or describe logical reasoning?

Hi Travis,

Suppose the chairs go in order starting at 1 and you got on chair 33. Behind you is chair 34 and behind that 35 and so on. When you get half way up the slope you notice chair 97 beside you. Thus the chairs numbered 34, 35, 36, ..., 97 Make up half the chairs. How many chairs are there?


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