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.

(In reply to re(2): 7 ways by Lisa)

I think 10 would get the same asterisk as 5.  I can be done only by placing one coin in the position where another vacated.  Consider the fact that any combination of rearranging all ten coins can be acheived by rearranging only 9.

This assumes that you can pick up all of the coins with out any additional constraints about remaining connected.

Cheers,
Will

Posted by Will on 2005-08-24 21:34:23