A piece of paper had the following diagram:

               o              o o o o
      From:   o o         To:  o o o
             o o o              o o
            o o o o              o

Below it, it read "Given the initial formation of ten coins, move exactly # coins to produce the end formation." It was pretty obvious that # stood for a digit, but it was smudged and couldn't be read. What possible numbers could it have been so the problem was solvable?

To allow explaining the solution, number the coins like this:

           0 
          1 2
         3 4 5
        6 7 8 9

Note: This problem was inspired by a forum question by Nicole.

3 moves:
      
6  1  2  9
  3  4  5
    7  8 
      0 

4 moves:

2  3  4  5
  6  7  8  
    9  1
      0

6 moves:

6  7  8  9 
  3  4  5
    1  2
      0

7 moves:

2  0  1  3
  5  4  6
    9  7
      8

8 moves:

5  0  1  2
  9  3  4
    6  7
      8

9 moves:
  
6  7  8  9
  3  4  5
    1  2
      0

10 moves:

9  8  7  6
  2  1  0
    4  3
      5

5 moves can't be done without exchanging a coin so really it doesn't work.

Posted by Lisa on 2005-08-15 09:04:48