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Sunday Times Teaser 3166 – All Their Marbles

by BRG on May 26, 2023

by Peter Good

Published Sunday May 28 2023 (link)

The original wording can be obtained by clicking the above link. What follows is a revision to remove ambiguities and clarify the intent of the original wording:

In their art class, Jack and Jill each had a box of spherical glass marbles of at least three different radii, each a whole number of centimetres.

Jack placed three identical marbles from his box onto a desk and then placed each of the others in turn on top with all four marbles touching. He worked out the height of the top of the upper marble above the desk, obtaining a different whole number of centimetres each time.

Jill was also able to do this with her marbles but they were all of different sizes to Jack’s.

None of the heights obtained were above 30 centimetres.

List all the different marble radii in ascending order.

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