## Teaser 2977: Enjoying retirement

**From The Sunday Times, 13th October 2019** [link]

George and Martha have worked on separate departments of a company which has four-digit telephone extensions. George looked at his extension and it was

ABCD. Martha’s (larger) also hadA,BandCas her first three digits but not necessarily in that order. Her last digit wasE. They added up their two four-digit numbers and found that the least significant digit wasF. They then looked at the difference and that was a four-digit number of which the least significant digit wasG. They then looked at the product and the least significant digit wasH. They then looked at the average of the extensions; in it the first two digits were equal, the last two digits were also equal, and the least significant digit wasJ. I have thus mentioned nine digits, all positive and unequal.What was Martha’s extension?

[teaser2977]

## Jim Randell 3:34 pm

on11 October 2019 Permalink |I assumed that the average of the two extension numbers was a whole number, so both extension numbers must have the same parity.

The following Python program runs in 92ms.

Run:[ @repl.it ]Solution:Martha’s extension number is 8563.George’s extension number is 6859.

So if George’s number is ABCD, then Martha’s is BCAE.

The sum is 15422, which ends in F=2.

The difference is 1704, which ends in G=4.

The product is 58733617, which ends in H=7.

And the average (mean) is 7711, which starts with two 7’s and ends with two J’s; J=1.

Each non-zero digit is mentioned once. We have (1, 2, 3, 4, 5, 6, 7, 8, 9) = (J, F, E, G, C, A, H, B, D).

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## GeoffR 9:31 am

on13 October 2019 Permalink |LikeLike