The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?
Note: The figure shown is representative.
To solve this problem, we need to determine the minimum number of bridges required to connect all five zones (Z1, Z2, Z3, Z4, and Z5) in the provided river system. This is essentially a graph theory problem, where each zone represents a vertex and each river segment represents an edge.
The goal is to find the smallest set of river segments that, if bridged, will allow crossing from any zone to any other zone. This can be thought of as finding a minimum spanning tree of the zones in the graph described by the river segments.
- List the connections needed:
- Z1 to Z2
- Z1 to Z4
- Z1 to Z5
- Z2 to Z3
- Z3 to Z4
- Z4 to Z5
- Explore the given options to find the set that connects all zones with the fewest bridges:
- Option Analysis:
- Bridges on P, Q, and T: Fails to connect Z2 and Z3.
- Bridges on P, Q, S, and T: Redundant connection with unnecessary S.
- Bridges on Q, R, T, and V: Connects all zones:
- Q connects Z1, Z2, and Z3 through R.
- Q and T connect Z1 to Z4.
- Q, T, and V connect Z3 to Z4.
- T connects Z4 to Z5 (via V).
- Bridges on P, Q, S, U, and V: Redundantly includes U without necessity for direct Z5 connection.
- Conclusion: The configuration with bridges on segments Q, R, T, and V connects all zones using the least number of bridges efficiently. Hence, the correct answer is Bridges on Q, R, T, and V.
Important Questions from Puzzles
- A thin wire is used to construct all the edges of a cube of $1 \text{ m}$ side by bending, cutting and soldering the wire. If the wire is $12 \text{ m}$ long, what is the minimum number of cuts required to construct the wire frame to form the cube?
In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.
1 1 2 2 X 3 2 X 4 1 2 X Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals).
As per this rule, the maximum number of crosses possible in the empty column is
In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.
The only movement allowed for a step involves, “two moves along one direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions marked X on the right.
Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is
In the 4 x 4 array shown below, each cell of the first three rows has either a cross (X) or a number.
1 X 4 3 X 5 5 4 3 X 6 X
The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is- The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:
• The line joining P and R is parallel to the line joining Q and S.
• P is placed on the side opposite to the corner T.
• S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?
