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 Four Crossed Female Athlete Ascertainment (Posted on 2022-11-11)
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)

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 computer solution Comment 2 of 2 |
clc
lines=perms('wxyz');

for i=1:length(lines)
line=lines(i,:);
if all(line([1 4])~='w')
w=strfind(line,'w');
x=strfind(line,'x');
y=strfind(line,'y');
for a=0:7
g(1)=a;
for b=0:7
g(2)=b;
for c=0:7
g(3)=c;
for d=0:7
g(4)=d;
srch=base+soc;
ix=find(g==srch);
if length(ix)==1
if ~any(bitand(g([w-1 w+1]),base))
nxtto=zeros(1,6);
for j=1:4
if bitand(g(j),soc)
nxtto([j j+2])=nxtto([j j+2])+1;
end
end
nxtto=nxtto(2:5);
f=find(nxtto==1);
if length(f)==1
if line(f)=='x'
nxtto=zeros(1,6);
for j=1:4
nxtto([j j+2])=nxtto([j j+2])+1;
end
end
nxtto=nxtto(2:5);
f=find(nxtto==1);
if length(f)==3
if line(10-sum(f))=='y'
disp(line)
disp(char(g+48))
disp(' ')
end
end
end
end
end
end
end
end
end
end
end
end

finds these 8 scenarios that fit:

zwxy
1106

zwxy
1506

yzwx
6031

yzwx
6071

yxwz
6011

yxwz
6051

xwzy
1306

xwzy
1706

The first line of each lists the order of the girls, by initial.

The second line in each case shows below each girl's initial, a number whose bits represent baseball (value 4), soccer (value 2) and basketball (1). In each case, Yvonne has a 6 (i.e. 4+2) below her initial, indicating she plays baseball and soccer but not basketball. No other girl has a 6 under her initial.

 Posted by Charlie on 2022-11-11 10:26:34

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