## Brainteaser 1635: Double anagram

**From The Sunday Times, 9th January 1994** [link]

In the woodwork class the

ABLESTstudents madeSTABLETABLES.In the arithmetic class the cleverest students took those three six-letter words which were anagrams of each other, and they then assigned a different digit to each of the six letters involved. Substituting letters for digits then gave them three six-figure numbers.

They found that one of the numbers was the sum of the other two. Furthermore, no matter what alternative substitution of digits they had used, they could never have achieved this coincidence with a lower sum.

(a) Which word was the sum?

(b) What was its numerical value?

This puzzle was included in the book *Brainteasers* (2002, edited by Victor Bryant). The text was changed slightly, but the puzzle remains the same.

[teaser1635]

## Jim Randell 8:37 am

on6 August 2019 Permalink |This program uses the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary to solve the alphametic problem, and an [[`Accumulator()`

]] object to find the smallest solution. It runs in 299ms.Run:[ @repl.it ]Solution:TABLES = 417582.The corresponding alphametic sum is:

ABLEST + STABLE = TABLES.There are 18 possible solutions to this alphametic.

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## GeoffR 1:29 pm

on6 August 2019 Permalink |I tried the three possible addition sums, looking for the smallest total. Two of these sums proved unsatisfiable. The third addition sum gave two possible values for TABLES, the smallest of which agreed with Jim’s solution.

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## John Crabtree 6:21 pm

on8 August 2019 Permalink |With TABLES as the sum, ABLE = 999(T-S) – 100S – 10T. This enables the desired solution, as well as all of the possible 18 found by Jim, to be easily found.

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