The Cathedral of St. Levikus has just purchased an ornate woodcarving with three rows to insert (one-sided) number cards, in order to inform the congregation of the hymns sung during the service.

Each of the 999 hymns in the cathedral's hymnal is labeled with a number (1 through 999). Three hymns are sung at each service, and no hymn will be sung more than once during each service.

The numbers on cards are written like this:

0 1 2 3 4 5 6 7 8 9

as they are on a computer's keyboard.

Given this information, how many number cards minimum are needed to correctly display any three different hymns?

If the font is the same as the sample numbers in the problem, 6's doubling as 9's will work, but 2's and 5's will not, leaving the answer at 64 digits.

Posted by hal on 2005-12-11 22:36:04