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 20050815 02:53:56 