I've just noticed that 18181 is valid too! (a rose is a rose is a rose) Best, É. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Eric Angelini Envoyé : lundi 26 janvier 2009 15:35 À : math-fun Objet : [math-fun] Coding + and = with digits inside an integer Hello Math-fun, ... stupid idea, yesterday, to get asleep: Let's examine a 5-digit integer like abcde; if we decide that b is the + sign and d the = sign, we have the simple equation a+c=e. This equation has a lot of solutions (like 1+2=3 or 1+0=1) ... but once we have decided that (for instance) 4 is coding "+" and 8 is coding "=", we cannot use elsewhere (in the integer) the digits 4 and 8. Thus, with the [4+;8=] convention, a valid 5-digit integer would be, for instance, 14283. Or 14081. Or 18041 (1=0+1). But not 24284 (2+2=+). Neither 04585 (no leading zero). Questions: a) What is the best [x+;y=] coding in order to produce the biggest quantity of valid 5-digit integers? b) Same question for a 6-digit integer? c) Same question for a 7-digit integer? (where 1424386 --> 1+2+3=6 would now be valid too!) Best, É. (now asleep) _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun