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

 Four Corners (Posted on 2004-07-17)
On each corner of a square is a quarter. Your task is to have all four quarter heads-up or tails-up at the end of a turn.

You are blindfolded at the start, and you do not know which are heads-up and which are tails-up. Each turn, you may flip however many of them you want and then ask if you are done (and no, you cannot tell, by touch, whether it is heads- or tails-up). The square is then rotated a random, undisclosed number of quarter spins (multiple of 90 degrees), and you may take another turn.

Minimize the maximum number of turns required to be assured you will complete the task.

 No Solution Yet Submitted by red_sox_fan_032003 Rating: 4.2500 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Good start | Comment 1 of 7

There are 4 combinations of heads and tails for the quarters, not including inversions and rotations.

`1  2  3  4HH TH TT THHH HH HH HT`

Likewise, there are also 4 combinations of flips that you can do each turn.

Each of the four combinations of flips can transform the four combinations of heads and tails to another combination (or the same combination). The chart below shows the possible resulting combination numbers, if you start with combination number shown on the top row and flip the combination number shown on the left column.

`  | 1   2  3  41 | 1   2  3  42 | 2 134  2  23 | 3   2 14  34 | 4   2  3  1`

Now, before minimizing the maximum, I'm going to try to just reach any maximum.

`Flip#| combin.# | possible results1    | 1        | 1,   2, 3,42    | 4        | -,   2, 3,13    | 3        | -,   2,14,-4    | 4        | -,   2,-1,-5    | 2        | -,1 34,--,-6    | 4        | -,- 31,--,-7    | 3        | -,-14-,--,-8    | 4        | -,--1-,--,-`

So I got it down to 8 turns.  Is it minimized?  I don't know.

Edited on July 17, 2004, 1:36 pm
 Posted by Tristan on 2004-07-17 13:31:26

 Search: Search body:
Forums (0)