## Teaser 2863: Little time

**From The Sunday Times, 6th August 2017** [link]

Do you have a little time to try this Teaser? I have taken a four-figure number and a six-figure number and I have consistently replaced digits by letters to give the words

LITTLEandTIME.If you take the digits of

TIMEand write down all the four-figure numbers which use exactly those digits in some order and then add up all those numbers, then your total will beLITTLE.What number is

TIME?

[teaser2863]

## Jim Randell 12:54 pm

on28 May 2020 Permalink |The puzzle text doesn’t include the usual alphametic caveat that different letters stand for different digits, only that the digits are replaced

consistentlyby letters (i.e. the same letter is replaced by the same digit). And if there are zero digits involved the 24 rearrangements of the 4 digits ofTIMEwill include some sequences which don’t give 4 valid digit numbers.So this Python program considers all 4 digit values for

TIME, and totals only those rearrangements corresponding to 4 digit numbers. It runs in 135ms.Run:[ @repl.it ]Solution:TIME= 3578.And so

LITTLE= 153318.It turns out that using a standard alphametic interpretation, and not worrying about whether the rearrangements always give 4 digit numbers will also give this answer. So:

If we write down the sum of the 24 permutations of

TIME, each letter appears in each column 6 times, the result of the sum is thus:Which we can solve as an alphametic expression using the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.The following run file gives the same solution in 92ms.

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## GeoffR 8:47 am

on29 May 2020 Permalink |Easy to check the digits in TIME give the digits in LITTLE

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