All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Hymn Numbers (Posted on 2005-12-07) Difficulty: 2 of 5
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?

See The Solution Submitted by Captain Paradox    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution re(2): First try -- a trick | Comment 3 of 6 |
(In reply to re: First try -- a trick by Old Original Oskar!)

You need 6 zeros (to display 100,200,300)

7 ones, twos, threes, fours, fives, sevens, eights (to display 111, 112, 113)

9 sixes that double as nines (to display 666, 669, 999)

All in all, 6+49+9=64 digits.

  Posted by e.g. on 2005-12-07 08:36:21

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information