In detail

The gondola lift

The gondola lift


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My friend Carmen and I are passionate about riddles and winter sports. The other day we went skiing and when I got on the cable car I came up with the following puzzle:

At the time I was sitting in cabin number 98, I crossed with chair number 105, while my friend Carmen who occupied cabin No. 241 crossed with No. 230. Of course, the cabins are regularly spaced over the cable and are numbered in order from No. 1.

How many cabins does this ski lift have?

Solution

In total there are 268 cabins in the cable car.

Between 98 and 241 there are 142 cabins including the previous two.
Between 230 and 105 there should be 105 + X - 230 + 1 cabins, the same as the previous ones.
So: 142 = 105 + X - 230 + 1 then X = 268