# Coin problem

• Jul 23rd 2009, 09:28 PM
Soroban
Coin problem

Nine coins are placed in 8 rows of 3 coins each.

$\displaystyle \begin{array} {ccccc} O &\to& O &\to& O \\ \downarrow & \searrow & | & \swarrow & \downarrow\\ O &\to& O &\to& O \\ \downarrow & \swarrow & \downarrow & \searrow & \downarrow \\ O &\to& O &\to& O \end{array}$

Move two coins and form 10 rows of 3 coins each.

• Jul 23rd 2009, 09:32 PM
VonNemo19
Is that 8 supposed to be a three? I'm not very good at this stuff, could you explain how there can be nine coins in 8 rows of three.
• Jul 24th 2009, 01:02 AM
Opalg
Quote:

Originally Posted by VonNemo19
Is that 8 supposed to be a three? I'm not very good at this stuff, could you explain how there can be nine coins in 8 rows of three.

"Row" here doesn't just mean a horizontal row, it refers to any three coins that are in a straight line. So there are three horizontal rows, three vertical rows and two diagonal rows.

• Jul 24th 2009, 04:06 AM
Wilmer
1 2 3
4 5 6
7 8 9
Put 4 and 6 on top of 5; then you have:
1 2 3
7 8 9
1 4 9
1 5 9
1 6 9
2 4 8
2 5 8
2 6 8
3 4 7
3 5 7
3 6 7

James F. Fixx: "everything that's not implicitly prohibited in a puzzle is allowed"
• Jul 24th 2009, 04:21 AM
Opalg
Quote:

Originally Posted by Wilmer
1 2 3
4 5 6
7 8 9
Put 4 and 6 on top of 5; then you have:
1 2 3
7 8 9
1 4 9
1 5 9
1 6 9
2 4 8
2 5 8
2 6 8
3 4 7
3 5 7
3 6 7

James F. Fixx: "everything that's not implicitly prohibited in a puzzle is allowed"

You're assuming that the coins have no thickness. (Evilgrin)
• Jul 24th 2009, 05:22 AM
Wilmer
Quote:

Originally Posted by Opalg
You're assuming that the coins have no thickness. (Evilgrin)

Mr Fixx says that ok !
• Jul 24th 2009, 06:55 AM
Soroban
This is the standard solution:

Spoiler:

$\displaystyle \begin{array}{ccccccccc} A & \to & \to & \to & B & \to & \to & \to & C \\ & \searrow && \swarrow & | & \searrow && \swarrow \\ & & D & \to & E & \to & F \\ & \swarrow && \searrow & | & \swarrow && \searrow \\ G & \to & \to & \to & H & \to & \to & \to & I \\ \end{array}$

Plus rows AEI and CEG.

• Jul 24th 2009, 10:07 AM
Wilmer
Ok, Soroban.

But if 11 instead of 10, do you agree mine is "acceptable"?