## Teaser 3046: Square phone numbers

**From The Sunday Times, 7th February 2021** [link]

George and Martha run a business in which there are 22 departments. Each department has a perfect-square three-digit extension number, i.e., everything from 100 (10²) to 961 (31²), and all five of their daughters are employees in separate departments.

Andrea, Bertha, Caroline, Dorothy and Elizabeth have extensions in numerical order, with Andrea having the lowest number and Elizabeth the highest. George commented that, if you look at those of Andrea, Bertha and Dorothy, all nine positive digits appear once. Martha added that the total of the five extensions was also a perfect square.

What is Caroline’s extension?

[teaser3046]

## Jim Randell 5:03 pm

on5 February 2021 Permalink |A simple Python program finds the solution in 67ms.

Run:[ @repl.it ]Solution:Caroline’s extension is 729.Manually, you can write out the squares, and then working through the possible candidates for A, B, D, the solution is discovered quite quickly.

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## GeoffR 7:51 pm

on5 February 2021 Permalink |LikeLike

## GeoffR 8:44 am

on6 February 2021 Permalink |LikeLike

## Frits 7:44 pm

on6 February 2021 Permalink |LikeLike

## Tony Brooke-Taylor 10:21 am

on7 February 2021 Permalink |LikeLike

## Frits 4:21 pm

on7 February 2021 Permalink |Logic can reduce a,b and d to specific squares.

The version without reduction logic is faster.

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## Frits 1:25 pm

on8 February 2021 Permalink |Not very efficient.

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