## Brainteaser 1538: Times square

**From The Sunday Times, 1st March 1992** [link]

Alf:Listen to this: “SUNtimesDAYequalsTIMES“.

Beth:Sounds like a lot of nonsense to me.

Alf:Let me write it down for you. Like this:

SUN × DAY = TIMESIn this sum are 10 different letters representing digits 0 to 9 and in my answer

SUNminusDAYis a perfect square. That should help you.

Beth:That’s a tall order, but I’ll have a go. Where’s my calculator.Beth did find Alf’s solution. What was their number for

TIMES?

This puzzle was selected for the book *Brainteasers* (2002, edited by Victor Bryant), in which it appeared in the following modified form:

With the usual letters-for-digits convention:

SUN – DAYis the square of a prime, and:

SUN × DAY = TIMESWhat number is

TIMES?

(We do not actually need to know that the square is the square of a prime, but it cuts down the work considerably).

[teaser1538]

## Jim Randell 7:38 am

on4 April 2019 Permalink |The wording (but not most of the meaning) of this Teaser was changed considerably for the book. In the original puzzle we were told that

(SUN – DAY)was a square number, but not that it was the square of a prime.The puzzle can be solved using the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.This run file executes in 235ms.

Run:[ @repl.it ]Solution:TIMES = 50862.We can remove the call to [[

`is_prime()`

]] to solve the original puzzle. The answer is the same.Without the subtraction constraint at all, the multiplication sum has three solutions:

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