# Sunday Times Teaser 1952 – Naturally Enough

*by Victor Bryant*

#### Published 13th February 2000

_ | 5 6 7 8 9

1 | ? ? ? ? ?

2 | ? ? ? ? ?

3 | ? ? ? ? ?

4 | ? ? ? ? ?

Imagine putting a digit into each of the 20 boxes of this grid so that, reading across, there are four five-figure numbers (labelled 1–4) and, reading down, five four-figure numbers (labelled 5–9). Do this in such a way that (naturally) the resulting numbers 1–9 have the following properties:

1, 4 and 9 are squares;

1 and 8 are cubes;

2, 3, 5 and 7 are primes;

6 is the product of two primes;

the average of 1–9 is more than 4.

You should then be able to answer the question:

What is the five-figure number forming 4 across?

2 Comments
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Faster for getting all solutions. It turned out that building dictionaries with a single comprehension statement slowed things down.