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Sunday Times Teaser 2829 – Making a Dozen

by Andrew Skidmore

Published: 11th December 2016 (link)

In this addition sum different letters consistently stand for different digits:

_____S E V E N
_____T H R E E
_________T W O
___T W E L V E

What is the value of LETTERS?

2 Comments Leave one →
  1. Brian Gladman permalink

    Using my alphametic sum solver AlphaSum (see here):

    Under normal circumstances, alphametic solvers based on column evaluation can be expected to be a lot faster than those based on permutations unless there are a large number of columns in the sum. On this occasion, however, the sum has a useful property in that the lower two columns and the upper 2/3 columns each involve only five letters. As a result we can split the permutation into two steps in a way that makes a solution much more efficient. Here is such a solution:

    The result is a permutation based solution that outperforms the column based solver by a factor of more than 3 to 1 – 17 milliseconds compared to 59 milliseconds (timed using Python profile).

  2. A straightforward Alphametic. We can solve it using the SubstitutedSum() solver from the library. This command runs in 164ms.

    The values for N and O can be interchanged, but we are asked for the value of LETTERS, so the solution is unique.

    The library is available at [ ].

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