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
# = 3 solutions by brianjn)
Had 'owl' not posted since my last response, I would have merely edited my comment.
I can further move 9 coins. Consider that one of the vertices of
the triangle be fixed, eg 9, then all other 9 coins need to be moved to
the right of the 9 and also below that line.
To 'owl', each of the solutions in my "# = 3 solutions" can be
accomplished by ensuring that the moved coin remains in contact with
one or two other coins; I actually visualised this in the documentation
of my solutions.
I shall not do this for this additional solution, but it may readily been seen that it is indeed possible.
If I consider the block of:
1 2
4 as immovable, an the
top left 'vertex' I can move 7 coins to form the desired inversion.
If I consider the group of:
8 9 as immovable, I can move 8 coins to create the desired array; two to the right and 6 below.
So, in all I have 3, 4, 6, 7, 8 and 9. Clearly I cannot have 1 or 2.
And 5? I could do this, but I would consider this to be an illegitimate solution:
If this 3 4 5
7 8 is my immovable block at
the top left of my array, I would have to move the 9 from its position
at some time and replace it with another coin  feel that that is not
in the spirit of the puzzle,
so,
I'll stay with 6 solutions; 3, 4, 6, 7, 8 and 9.

Posted by brianjn
on 20050815 05:47:15 