Question

Who is standing at intersection a? 

• A. No one
• B. V
• C. W
• D. Y
• A. U only
• B. U, W and Z only
• C. U and Z only
• D. Z only
• A. 2
• B. 3
• C. 1
• D. 4
• A. U and Z only
• B. V and X only
• C. W and X only
• D. U and W only

Answer 1

The Correct Option is A

The problem requires determining who is standing at intersection a using logical deduction based on the given conditions.

Let's analyze the provided facts:

• X, U, and Z form a triangle where they are the only people at the three corners.
• X can see only U and Z, implying X must be on an edge, with U and Z on direct lines.
• Y can see only U and W, restricting Y's position to a line with U and W, but not with Z or V.
• U sees V behind Z, suggesting V is on a line further from U's perspective behind Z.
• W can't see V or Z, so W mustn't be on interconnected lines with them.
• No one is at intersection d.

Let's place each person logically:

1. X, U, and Z form a triangle; possible corners: X at f, U at g, Z at e. X can see U (g) and Z (e).
2. V needs placement where U can see it behind Z. Possible placement: V at l, seen from g through e.
3. Y sees only U and W: potential positions are i for Y, seeing U at g and W at j.
4. W at j fulfills not seeing V or Z.

Examining the intersections:

• a: No one remains unplaced among U, V, W, X, Y, and Z.

Thus, the intersection a is not occupied by anyone, making the correct answer: No one.

Answer 2

The problem involves identifying who individual V can see given specific constraints in a street intersection map. Let's resolve this step by step using the provided conditions: 

1. X, U, and Z form the corners of a triangle on the street map, indicating they are connected by street segments.

2. X can see only U and Z, suggesting that X is possibly at a corner with unobstructed sight to intersections U and Z exclusively.

3. Y's sight is limited to U and W, indicating that Y is at an intersection in line with U and W but not further lines of sight such as V or Z.

4. U has a direct line of sight to V, positioned behind Z relative to U. This implies Z is between U and V along a straight line.

5. W cannot see V or Z, meaning W's position intercepts lines leading to those points.

6. No one is located at intersection d.

Given the constraints above, for V's placement: V is positioned directly in line with U and Z such that U sees Z and V behind Z.

Intersections	Sighted Individuals
X	U, Z
Y	U, W
U	V (behind Z)
W	No V or Z

From the above, V can see U and Z directly because they share a linear alignment, confirming the correct answer: "U and Z only".

Answer 3

The problem asks us to determine the minimum number of street segments that X must cross to reach Y, based on provided constraints.

Below is the reasoning: 

• People are standing at different intersections with no two people standing at the same intersection.
• X, U, and Z form a triangle with three street segments, meaning they are positioned at three intersections that create a triangular path.
• X can only see U and Z, indicating X is at one corner of the triangle.
• Y can only see U and W, suggesting Y is positioned in line with these intersections.
• U sees V in the next intersection behind Z, aligning V in the visual path behind Z from U's perspective.
• W cannot see V or Z, limiting W's line of sight to other specific intersections.

To deduce the street segments X must cross to reach Y, consider:

• The triangle comprises the intersections of X, U, and Z exclusively. Since X can only see U and Z, X’s movement to any other intersection must involve crossing a segment not part of the triangle.
• To move toward Y, X must cross either directly to U or Z first, then navigate through additional segments to align with Y’s line of visibility, incorporating intersections that allow visual contact with U and W.

Considering these deductions, the minimum street segments X must cross to align the path toward Y, taking optimal routes and respecting line of sight constraints, is 2.

Options	Intersection Strategy
1	Requires an unobstructed line sight which isn't feasible here.
2	Optimal path as explained above.
3	Requires crossing one extra, unnecessary segment.
4	Exceeds the needed path and involves indirect navigation.

Hence, the minimum number of street segments X must cross to reach Y is 2.

Answer 4

Valid Configuration: 
Case (v) is the only valid one.

Explanation

• U is at g
• Z is at f
• V is at e

This satisfies the condition: \( U \rightarrow Z \rightarrow V \) are in a straight line.

X must be at b because X can see only U and Z (positions g and f).
Hence, no one is at positions: a, c, j.

W cannot be at h or i because W cannot see Z or V.
Thus, W must be at I.

Y must see both U and W. The only valid position for Y to see both g and I is from k.

✅ Final Positions

Person	Position
X	b
U	g
Z	f
V	e
W	I
Y	k

All conditions are satisfied in this configuration.

If a new person is standing at d, that person can see W and X. Answer: (W and X only)