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

Home > Just Math
Tile flipping (Posted on 2015-04-08) Difficulty: 3 of 5
A puzzle consists of a number of tiles, T, colored red on one side and blue on the other.

Start with all red side up. The goal is to get them all blue side up in the fewest number of rounds.
A round consists of flipping exactly N of them.

Find a rule for when the puzzle is impossible for given values of (T,N) with N≤T.

Find a rule for the number of rounds it will take when the puzzle is possible.

No Solution Yet Submitted by Jer    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts N = 3 | Comment 7 of 12 |
Well, nobody has tried yet to find a rule for the number of rounds it will take.

As a start, I considered N = 3.

When T = 3k, it will take k turns.

When T = 3k+1, the minimum possible is obviously k + 1 turns, where one tile is flipped 3 times and the remaining 3k tiles are flipped once.  But this is not possible if T = 4, because this scheme requires 2 "once-flipped" tiles to be flipped each time the "thrice-flipped" tile is flipped, and there are only 3 "once-flipped" tiles available .  (T,N) = (4,3) requires 4 flips.

When T = 3k+2, the minimum possible is obviously k + 2 turns, where two tiles are flipped 3 times and the remaining 3k tiles are flipped once.  This does work for T = 5, because with this scheme only one "once-flipped" tile needs to be flipped on each turn.  

So for N = 3, the formula is 
When T < 3    IMPOSSIBLE
When T = 4    4
Otherwise      FLOOR(T/3) + MOD(T,3)

Edited on April 10, 2015, 12:55 pm
  Posted by Steve Herman on 2015-04-10 10:18:33

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 (2)
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