Four girls, Willow, Ximena, Yvonne, and Zelda, are standing in a line. Exactly one girl plays baseball and soccer but not basketball.

The following facts are known:

- Two girls who do NOT play baseball are standing next to Willow.
- Ximena is the only girl standing next to exactly one soccer player.
- Yvonne is the only girl NOT standing next to exactly one basketball player.

Who plays baseball and soccer, but not basketball?

Answer is Yvonne.

Assume orientation L to R does not matter.

**From 1.** the lineup is one of X__Z, X__Y, Y__Z

Each has two possibilities. Say nB means not baseball, nK not basketball, and nS not soccer.

The possibilities are these

1 (XWYZ) = (nB W nB Z)

2 (XYWZ) = (X nB W nB)

3 (XWZY) = (nB W nB Y)

4 (XZWY) = (X nB W nB)

5 (YWXZ) = (nB W nB Z)

6 (YXWZ) = (Y nB W nB)

**From 2**. The situation must be

(? ? X ?) = (nS nS nS S)

(X must be 2nd from the end and the only S player is on that end.)

We are down to possibilities 5. and 6.

5. (YWXZ) = (nB,nS nS nB,nS S)

6. (YXWZ) = (S nB,nS nS nB,nS

**From 3.** The only configuration is:

(Y ? ? ?) = (nK nK K K)

So 5 and 6 become:

5. (Y W X Z) = (nB,nS,nK nS,nK nS,nB,K S,K)

6. (Y X W Z) = (S,nK nS,nB,nK nS,K nB,nS,K)

The only yes-Soccer and no-Basketball player can be found in configuration 6, **featuring Yvonne**

*Edited on ***November 11, 2022, 6:45 pm**