## Teaser 2969: Slide rules

**From The Sunday Times, 18th August 2019** [link]

Using her ordinary 15cm ruler and Zak’s left-handed version (numbers 1 to 15 reading right to left) Kaz could display various fractions. For instance, putting 5 on one ruler above 1 on the other ruler, the following set of fractions would be displayed: 5/1, 4/2, 3/3, 2/4 and 1/5. Zak listed the fifteen sets starting from “1 above 1” up to “15 above 1”.

Kaz chose some fractions with values less than one from Zak’s sets (using just the digits 1 to 9, each once only in her selection). Of these, two were in simplest form, one of which had consecutive numerator and denominator. Zak correctly totalled Kaz’s selection, giving the answer as a fraction in simplest form. Curiously, the answer’s numerator and denominator were both palindromic.

Give Zak’s answer.

[teaser2969]

## Jim Randell 10:45 pm

on15 August 2019 Permalink |This Python program collects possible fractions, and then uses a recursive function to select viable sets that Kaz could have chosen. These sets are then examined to find candidates where the sum is expressed as a fraction consisting of two palindromes.

Run:[ @repl.it ]Solution:Zak’s answer is 545/252.The fractions Kaz has chosen are:

There are 10 sets of fractions that Kaz could have chosen, but only one of these sets has a total consisting of palindromic numerator and denominator when expressed in lowest terms.

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