From: anaha@hotmail.com
Newsgroups: sci.math
Subject: "des chiffres et des lettres"
Date: Fri, 29 May 1998 08:05:12 GMT

There is a famous game in France called "des chiffres et des lettres", ie.
"letters and numbers". The "numbers" part is s follows :

seven numbers are chosen at random in the set {1,2,...,9,10, 25, 50, 75, 100}
and another number between 1 and 999 is also picked at random.

Then we have to obtain this number with the seven others and the four
operations, using each number only once.

I can not see clearly what mathematics are implied here, and it would bevery
nice if someone had an idea of an algorithm to see if there is a solution and
generate it. Oh, I forgot : the players have 40 seconds, which is not very
long, nd a brutal algorithms would maybe bee to slow.

thanks for any suggestion...

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From: Torkel Franzen <torkel@sm.luth.se>
Newsgroups: sci.math
Subject: Re: "des chiffres et des lettres"
Date: 29 May 1998 11:16:18 +0200

anaha@hotmail.com writes:

 > seven numbers are chosen at random in the set {1,2,...,9,10, 25,
 > 50, 75, 100} and another number between 1 and 999 is also picked at
 > random.
 > Then we have to obtain this number with the seven others
 > and the four operations, using each number only once.
 > ...
 > Oh, I forgot : the players have 40 seconds, which
 > is not very long, nd a brutal algorithms would maybe bee to slow.

  This is the sort of game that should be left to computers:


find_expression(L,U,N):-
        expression(L,U),
        N is U.

expression([X],X):-!.
expression(L,U):-
        pick(X,L,Lrest),
        expression(Lrest,U1),
        combine(X,U1,U).

combine(X,U1,X*U1).
combine(X,U1,X+U1).
combine(X,U1,X-U1).
combine(X,U1,U1-X).
combine(X,U1,X//U1):-W is U1,W\==0,0 is X mod W.
combine(X,U1,U1//X):-X\==0,0 is U1 mod X.

pick(X,[X|L],L).
pick(X,[Y|L],[Y|L1]):-
        pick(X,L,L1).


  Example:

| ?- find_expression([75,8,3,50,7,4,6],U,393).

U = 7*(50+(6+3*4))-8-75 ? 

yes
| ?- find_expression([75,8,3,50,7,4,6],U,45). 

U = 75-(8+(3+(50-(7+4*6)))) ? 

yes
| ?- find_expression([75,8,3,50,7,4,6],U,1). 

U = 3+(50+(7+4*6))-8-75 ? 

yes
| ?- find_expression([75,8,3,50,7,4,6],U,783).

U = 75+(8-50*(3+(7-4*6))) ? 

yes