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.

Move 6 to contact 0 and 1.
Move 3 to contact 0 and 2.
Move 7 to contact 2 and 5.
Lastly move 9 to contact 3 and 7.

6 0 3 9
 1 2 7
  4 5
   8

I could also move, just 3.
Rotate the digits 0, 6 and 9, either clockwise, or anticlockwise.
6 1 2 0          0 1 2 9
 3 4 5             3 4 5
  7 8                7 8
   9                   6

But then I could move 6.  I am keeping the line 0, 2, 5 and 9 intact:

0 6 1 8
 2 3 4
  5 7
   9

Certainly other representations of these 3 solutions are possible.
Although it was not suggested in the notes, I have assumed that a moved coin must stay in contact with at least one other coin whilst being moved to the new position.

I have 4, 3 and 6.

Posted by brianjn on 2005-08-15 02:53:56