# Math Help - We can't agree....

1. ## We can't agree....

Each of three colored cups covers one of these objects

1. The red cup is somewhere to the left of the white cup
2. The coin is somewhere to the left of the bean
3. The gray cup is somewhere to the right of the shell
4. The bean is somewhere to the right of the gray cup.

Under which color cup is the shell?

Thanks for looking!

2. Hello, fecoupefe!

This is a very simple "logic problem".

Each of three colored cups (red, white, gray) covers one of these objects: coin, bean, shell.

1. The red cup is somewhere to the left of the white cup
2. The coin is somewhere to the left of the bean . . . . unnecessary
3. The gray cup is somewhere to the right of the shell
4. The bean is somewhere to the right of the gray cup.

Under which color cup is the shell?
There are three colors: Red, White, Gray.
There are three objects: Coin, Bean, Shell.
There are three positions: Left, Middle, Right.

Statement 3: . $\text{(Shell)} \to \text{(Gray)}$

Statement 4: . $\text{(Gray)} \to \text{(Bean)}$

So we have: . $\underbrace{\text{(Shell)}}_L \to \underbrace{\text{(Gray)}}_M \to \underbrace{\text{(Bean)}}_R$

Statement 1: . $\text{(Red)} \to \text{(White)}$
Since Gray is in the middle, Red is on the Left, White is on the RIght.

And we have: . $\begin{bmatrix}\text{Red}\\ \text{Shell} \\ L \end{bmatrix}\;\;\begin{bmatrix}\text{Gray} \\ \text{Coin} \\ M \end{bmatrix}\;\;\begin{bmatrix}\text{White} \\ \text{Bean} \\ R \end{bmatrix}$

Statement 2 was not needed . . .
.

3. ## Well, Soroban...

I wish I had your "logical" mind. My 8 yr old had said it was Red, but I thought it was white. He thanks you for agreeing with him. I thank you for a wonderful explanation!