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 is- Three children P, Q, R and two grown-ups X, Y play a badminton doubles tournament. X and Y are parents to two of the children playing. The child of X is not the same as the child of Y. Exactly one of the children does not have a parent playing in the tournament. The following rules are followed:
(i) A parent and his/her child cannot be on the same team.
(ii) A match can feature at most one parent and his/her child, that is, a maximum of one parent-child pair can play in a match.
The following matches were played:TEAM 1 TEAM 2 MATCH 1 P and X Q and R MATCH 2 P and R X and Y MATCH 3 R and X Q and Y
Which one of the following options is correct? - Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that:
(i) the first game was the only game where two students of the same class played against each other,
(ii) the students of Class 5 won more games than the students of Class 4, and
(iii) the boys won two games and the girls won one game.
The student who did not lose any game is __________. - In the 2020 summer Olympics’ Javelin throw finals, Neeraj Chopra exhibited a spectacular performance to win the gold medal. The silver medal was won by Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were six rounds of throws with each athlete having one throw per round. The best of all the throws of each athlete is considered for the medal. Following were the observations about the throws:
i. The first and second rounds were dominated by Neeraj Chopra with a gold medal performance in his second throw, while the other two athletes did not have any medal winning throws in these rounds.
ii. The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely were fouls and were not considered for scoring.
iii. After four rounds, Vitezlav Vesely was in the second position and could not improve upon his best throw in the succeeding rounds.
iv. In the fourth round, the throw by Jakub Vadlejch was the best in that round.
In which round did Vitezlav Vesely have his best throw? Students 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
