P is a 17 digit positive integer and Q is obtained by writing the digits of P backwards. If neither P nor Q has leading zeroes, can P+Q include no even digits?

the only way you can find P such that P+Q has no even digits is at a roulette table, this is because in all other circustances 0 is considered even (try betting even, you lose if the ball lands on 0).  This is because 17 has a middle digit which is the 9th digit.  That digit does not change position upon reversal so if the 9th digit of P is d then the 9th digit of P+Q is 2d and therefore P+Q will always contain at least 1 even digit.  Now if P were to have had an even number of digits, i.e 4, then it would be possible with an example like 1122+2211=3333.

Posted by Daniel on 2007-08-15 11:17:45