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

Home > Shapes
Unit Cubes (Posted on 2004-02-02) Difficulty: 3 of 5
Some unit cubes are assembled to form a larger cube. Some of the faces of the larger cube are then painted. The cube is taken apart and it is found that 217 of the unit cubes have paint on them. What is the total number of unit cubes?

See The Solution Submitted by Brian Smith    
Rating: 3.8333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Extension (A deeper question) | Comment 9 of 15 |
I like this problem a lot, although I've seen variations before.

The most interesting variations (In my opinion) have a missing number that gives multiple possibilities.

217 has only a single possibility for cube size and method of side painting.

If you are told that 8 sides have paint on them, there are 5 possible ways of painting a 2x2x2 cube, so this isn't very interesting.

There are plenty of examples with two possible size & pattern cominations. For example: 91

My question are there any numbers that could yield a lot of solutions? There are 8 ways of painting up to 5 sides of a cube, but some are mutually exclusive, so there can't be 8 solutions. How many can there be?

-Jer
  Posted by Jer on 2004-02-04 11:26:12
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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information