Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch over the walkways that join at that junction. The minimum number of guards needed to watch all the walkways is ________.
To determine the minimum number of guards needed to watch all the walkways in the art gallery, we must consider the coverage provided by placing a guard at each junction (black dot).
The key is to ensure that every walkway is under surveillance without unnecessary overlap. This requires smart placement of guards at strategic junctions.
- First, identify all the junctions in the diagram. Each junction is a point where two or more walkways meet.
- The goal is to minimize the number of guard placements while covering all walkways connecting the junctions.
- In this particular diagram, consider which junctions allow for maximal coverage:
- Start by placing a guard at the top junction. This will cover the two walkways connecting to adjacent junctions.
- Next, place a guard at one of the bottom junctions. This covers the walkways adjacent to the bottom row.
- Finally, place a guard at the remaining junction to ensure all walkways are monitored.
- Therefore, the minimum number of guards required is 3.
The correct answer is 3, as it ensures all junctions are covered with the least number of guards.
Important Questions from Puzzles
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 isStudents applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. Preferences of lower ranked applicants are ignored during allocation.
Given the data below, which room will Ajit stay in?Names Student seniority Current room Room preference list Amar 1 P R, S, Q Akbar 2 None R, S Anthony 3 Q P Ajit 4 S Q, P, R 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.
- 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? 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
