## Teaser 3008: Three-fruit fractions

**From The Sunday Times, 17th May 2020** [link]

The owner of the old curiosity shop repaired an antique mechanical fruit machine having three wheels of identical size and format. Afterwards each wheel was independently fair, just as when new. Each wheel’s rim had several equal-sized zones, each making a two-figure whole number of degrees angle around the rim. Each wheel had just one zone showing a cherry, with other fruits displayed having each a different single-figure number (other than one) of zone repetitions.

Inside the machine were printed all the fair chances (as fractions) of getting three of the same fruit symbol in one go. Each of these fractions had a top number equal to 1 and, of their bottom numbers, more than one was odd.

What was the bottom number of the chance for three cherries?

[teaser3008]

## Jim Randell 7:26 am

on16 May 2020 Permalink |I assumed the wheels are identical duplicates of each other, which gives a unique solution.

This Python 3 program runs in 87ms.

Run:[ @repl.it ]Solution:There is a 1 / 5832 chance of getting 3 cherries.Each wheel is divided into 18 sectors. Each sector subtends 20°.

There are 4 fruits, each is allocated 1, 2, 6, 9 sectors on each wheel.

The probabilities for each of the 4 fruits are: 1/5832 (= 1/18³), 1/729 (= 1/9³), 1/27 (= 1/3³), 1/8 (= 1/2³).

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