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.

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

**Question 1: **

Who is standing at intersection a?

- No one
- V
- W
- Y

**Show Answer**

**1**

**Question 2: **

Who can V see?

- U only
- U, W and Z only
- U and Z only
- Z only

**Show Answer**

**3**

**Question 3: **

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

- 2
- 3
- 1
- 4

**Show Answer**

**1**

**Question 4: **

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

- U and Z only
- V and X only
- W and X only
- U and W only

**Show Answer**

**3**

It is given that X, U and Z are standing at the three corners of the triangle formed by three street segments. This means X, U and Z are standing at b, c. g or b, f, g. not necessarily in that order.

It is given that U sees V standing in the next intersection behind Z. This means U, V and Z are in a straight line with Z being in between U and V. The possibilities for this are:

(i) U, Z and V standing at b. f and j respectively. In this case, X is at g. Since X can only see U and Z, no one is standing at e. h and k. For Y to be able to see U and W, Y has to be at a and W has to be at i. But in this case, W will be able to see V, which is not valid. Hence, this case is not possible.

(ii) U, Z and V standing at b, c and d respectively. This is not possible because nobody is standing at d.

(iii) U, Z and V standing at c. b and a respectively. In this case. X is at g. Since X can only see U and Z. no one is standing at e, f. h and k. In this case. Y will not be able to see U. Hence, this is not possible.

(iv) U, Z and V standing at c. g and k respectively. In this case, X will be at b. Since X can only see U and Z, no one is standing at a. f and j. In this case. Y will not be able to see U. Hence, this is not possible.

(v) U, Z and V standing at g. f and e respectively. In this case, X will be at b. Since X can only see U and Z. no one is standing at a, c and j. W cannot see V or Z. Therefore. W cannot be at h or i. So W will be at k or I.

If W is at k, Y will be at h, i or I. In none of these three places can Y see both U and W.

Therefore. W is at I. For Y to be able to see only U and W, Y has to be at k.

(vi) U, Z and V standing at f, g and h respectively. In this case, X will be at b. Since X can only see U and Z, no one is standing at a, c and j. For Y to be able to see U. Y has to be at e. But in this case, Y will be able to see Z and V as well. But Y can only see U and W. Hence, this is not possible.

People are standing in the following way:

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