The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections. For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.

Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.
The following additional facts are known.

1. X, U, and Z are standing at the three corners of a triangle formed by three street segments.
2. X can see only U and Z.
3. Y can see only U and W.
4. U sees V standing in the next intersection behind Z
5. W cannot see V or Z.
6. No one among the six is standing at intersection d.

Q.1 Who is standing at intersection a?

1. V
2. W
3. No one
4. Y

explanation

Answer: 3

X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.
Now X cannot be at g since he sees only 2 people.
UZV have to be in a straight line and x sees only U and z thus
X must be at b, V at e, Z at f, U at g.
Since Y can see W and W cannot see either V or Z thus
Y must be at k and W must be at at l.
–   V   –
X   Z   –
–   U   Y
–   –   W
Now all questions can be answered

Q.2 Who can V see?

1. U and Z only
2. Z only
3. U only
4. U, W and Z only

Explanation

Answer: 1

Solution:
X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.
Now X cannot be at g since he sees only 2 people.
UZV have to be in a straight line and x sees only U and z thus
X must be at b, V at e, Z at f, U at g.
Since Y can see W and W cannot see either V or Z thus
Y must be at k and W must be at at l.
–   V   –
X   Z   –
–   U   Y
–   –   W
Now all questions can be answered.

Q.3 What is the minimum number of street segments that X must cross to reach Y?

1. 1
2. 2
3. 3
4. 4

explanation

Answer: 2

Solution:
X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.
Now X cannot be at g since he sees only 2 people.
UZV have to be in a straight line and x sees only U and z thus
X must be at b, V at e, Z at f, U at g.
Since Y can see W and W cannot see either V or Z thus
Y must be at k and W must be at at l.
–   V   –
X   Z   –
–   U   Y
–   –   W
Now all questions can be answered.

Q.4 Should a new person stand at intersection d, who among the six would she see?

1. W and X only
2. U and W only
3. V and X only
4. U and Z only

Answer: 1