## Brain-Teaser 481

**From The Sunday Times, 16th August 1970** [link]

The houses in Long Lane are conventionally numbered; odd on one side, even on the other. Six of my friends, all of different professions, live there, all except Black on the same side of the road. Each man’s house has a two-digit number, and the sum of the twelve digits, which is a perfect square, equals the number of the solicitor’s house. One house, next door to Robinson, is vacant.

Reversing the digits of the number of Robinson’s house give the number of the doctor’s house. Both numbers are primes. The two extreme numbers of the six are occupied by Jones and the dentist.

Reversing the digits of Green’s house gives the number of the architect’s house, and the difference between the squares of these is the square of the number of journalist’s house. Smith and the stockbroker live next door to each other.

What is the number of the vacant house? What is White’s profession? And what is the name of the stockbroker?

[teaser481]

## Jim Randell 9:46 am

on30 May 2019 Permalink |There are quite a few conditions. I started with the two conditions that deal with reversing one of the house numbers to get another number. Together these conditions give us the house numbers for two of the names and three of the jobs, so we can work out what the majority parity of the numbers is and fill out the remaining numbers appropriately.

This Python program runs in 96ms.

Run:[ @repl.it ]Solution:The vacant house is number 29. White is the Solicitor. Robinson is the Stockbroker.The solution is completely determined:

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