## Brainteaser 1510: Sum puzzle

**From The Sunday Times, 18th August 1991** [link]

In this addition sum nine digits are each represented by a different letter and the remaining one digit it represented in various places by nine letters.

When the 47-figure number:

INTHISADDITIONSUMNINEDIGITSAREEACHREPRESENTEDBYis added to the 46-digit number:

ONELETTERANDONEDIGITISREPRESENTEDBYNINELETTERSthe answer is the 47-figure number:

TDODRRITECIPADAABSDLOTRSORANOHMIAGSAOTUDAYDOEOEWhat is the

SOLUTION?

The text of this puzzle is taken from the book *Brainteasers* (2002, edited by Victor Bryant), so may differ from the puzzle originally published in the newspaper.

[teaser1510]

## Jim Randell 7:11 am

on30 March 2019 Permalink |Potentially we could just feed the entire sum as a single expression to the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary, but generating and considering all the possibilities for the 15 digits in the terms of the sum is going to take some time.So to help it along I provided some additional expressions, which are the sums formed taking some of the columns (in pairs, to reduce the amount of typing), linked together by carries. After 9 pairs we have mentioned each letter at least once, and the solver finds the solution in less than 200ms.

This run-file executes in 183ms.

Run:[ @repl.it ]Solution:SOLUTION = 78665482The assignment of letters to digits is:

so the sum is:

This is the only solution, even if the 18 symbols are grouped together differently (i.e. not 9 symbols standing for 1 digit each, and 9 all standing for the same remaining digit).

LikeLike