## Brain-Teaser 469

**From The Sunday Times, 24th May 1970** [link]

Before his retirement, the Master Spy, enigmatic to the last, left instructions for opening his safe and recovering the Top Secret plans for Winning World Domination:

“The combination is a 7-figure number, the sum of whose digits is 55. The first 4 figures make up a number divisible by 17, the sum of whose digits is also divisible by 17. The last 3 figures make up a number divisible by 7, the sum of whose digits is also divisible by 7.

By now you should realise that there are 4 possible combinations. Since 3 of these all detonate a booby-trap, I’d better warn you that the correct number has no figure appearing more than 3 times”

What is the combination of the safe?

[teaser469]

## Jim Randell 8:23 am

on9 April 2019 Permalink |We can treat this puzzle as a collection of alphametic expressions that can be handled by the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.The following run file executes in 324ms.

Run:[ @repl.it ]Solution:The combination is 9979588.The four candidate numbers are: 9979777, 9979588, 9979966, 9979399.

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## GeoffR 3:07 pm

on9 April 2019 Permalink |LikeLike

## Jim Randell 5:18 pm

on9 April 2019 Permalink |And we could add the following constraint to narrow the possibilities down to the single answer:

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