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 Inverting Triangles (Posted on 2005-08-15)
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.

 No Solution Yet Submitted by Erik O. Rating: 2.1667 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 # = 3 solutions | Comment 2 of 14 |
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

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