## Teaser 2818: Accountability

**From The Sunday Times, 25th September 2016** [link]

George and Martha’s bank account number is an 8-digit number consisting of the digits 1 to 8 in some order.

Martha commented that, if you split the number into two 4-figure numbers, then the number formed by the last four digits is a multiple of the number formed by the first four digits.

Then George listed all the different prime numbers that divided exactly into the account number. When he added together all those primes the total was less than a hundred.

What is their account number?

[teaser2818]

## Jim Randell 12:01 pm

on26 August 2019 Permalink |We can solve this puzzle using the general alphametic solver [[

`SubstitutedExpression()`

]] from theenigma.pylibrary.The following run file executes in 218ms.

Run:[ @repl.it ]Solution:The account number is 12876435.The number factorises as:

So the sum of the prime divisors is 84.

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