# Math Help - Coin problem

1. ## Coin problem

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

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

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

2. 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.

3. 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.

Spoiler:

4. How about 11 rows:
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"

5. Originally Posted by Wilmer
How about 11 rows:
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.

6. Originally Posted by Opalg
You're assuming that the coins have no thickness.
Mr Fixx says that ok !

7. This is the standard solution:

Spoiler:

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

Plus rows AEI and CEG.

8. Ok, Soroban.

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