Enigmatic Code
Programming Enigma Puzzles
Enigma 226: Cold comfort five
Posted by on 2 October 2014
From New Scientist #1372, 25th August 1983 [link]
In the following fully-worked division, all the digits have been replaced by blanks except for one. And before you start counting your blessings in having at least one digit to go on, I must tell you that the 5 is, in fact, wrong.
What is the five-digit quotient?
Note: I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment.
[enigma226]
Enigmatic Code 
This Python program uses the [[
SubstitutedDivision()]] solver from the enigma.py library. It runs in 699ms.from enigma import SubstitutedDivision, printf p = SubstitutedDivision( '???0000', '??', '?????', [('???', '??', '?'), ('??', '??', '??'), ('???', '?5?', '??'), ('???', '???', '??'), ('???', '???', '')], { '0': 0 } ) # "5" can't stand for 5 for s in p.solve(lambda s: s.d['5'] != 5): p.solution(s) (q, r) = divmod(s.c, 10000) printf("quotient = {q}.{r:04d}")Solution: The quotient is 2.1875.
The new [[
SubstitutedDivision()]] solver in the enigma.py library is derived from the [[SubstitutedExpression()]] solver, so can use the same solver parameters that it does. This means that we can provide the condition that the digit specified is not 5 directly to the solver, rather than reject general solutions where it does stand for 5 at the end.Here is a run file problem that executes in 259ms.