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 7 ways by Lisa)

I hedged about declaring 5 moves as a solution because I would have, in due course, placed another coin in the same position as another.

From your last comment Lisa, including the bolding of numerals, I have to assume that every coin in the "10 moves" has a uniquely new position. Yes?  

Erik O. did not give us any rules, I 'put in place' one that I knew had been used in similar coin puzzles.  

As you have allowed for all 10 coins to have been moved, where was the original layout in relation to your last proposal?  (I made an assumption that part of the array had to be 'intact', but Erik O did not say that, did he?)

Another question, and Erik O did not preclude this:
(original layout)
           0
          1 2
         3 4 5
        6 7 8 9
      have you at any time, in any of your solutions removed a coin like, 2 or 5, which has two lineal "adjacent" neighbours?   2 is bounded by 0 and 5, 5 is bounded by 2 and 9.

Just for my own clarity, and those of others who may follow, what rules did you consider yourself to be bound?

Posted by brianjn on 2005-08-15 13:23:41