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Four Crossed Female Athlete Ascertainment (Posted on 2022-11-11) Difficulty: 3 of 5
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:

  1. Two girls who do NOT play baseball are standing next to Willow.
  2. Ximena is the only girl standing next to exactly one soccer player.
  3. Yvonne is the only girl NOT standing next to exactly one basketball player.
Who plays baseball and soccer, but not basketball?

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
soln | Comment 1 of 2

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
  Posted by Steven Lord on 2022-11-11 09:31:16

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