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
Grid Puzzle Analysis
The problem involves a 4x4 grid where cells contain either a cross ('X') or a number. A number indicates the count of its adjacent neighbors (including diagonals) that are *not* crosses. We are given the first three rows and know the last row contains only numbers. The goal is to find the sum of these numbers in the last row.
Visualizing the 4x4 Grid
The provided string '1X43X5543X6X' represents the first three rows of the grid. Let's visualize it:
| C1 | C2 | C3 | C4 | |
| R1 | 1 | X | 4 | 3 |
| R2 | X | 5 | 5 | 4 |
| R3 | 3 | X | 6 | X |
| R4 | N1 | N2 | N3 | N4 |
Here, N1, N2, N3, and N4 are the unknown numbers in the last row (R4).
Understanding the Neighbor Rule
The core rule is: the number in a cell equals the count of its non-'X' neighbors. Neighbors include cells directly adjacent horizontally, vertically, and diagonally.
Calculating Last Row Numbers
We calculate N1, N2, N3, and N4 by checking their neighbors:
- N1 (Cell R4, C1): Its neighbors are R3C1 (value 3), R3C2 (value X), and R4C2 (value N2). The non-'X' neighbors are R3C1 and R4C2 (since R4 has only numbers). Thus, N1 counts 2 non-'X' neighbors. So, N1 = 2.
- N2 (Cell R4, C2): Its neighbors are R3C1 (3), R3C2 (X), R3C3 (6), R4C1 (N1), and R4C3 (N3). The non-'X' neighbors are R3C1, R3C3, R4C1, and R4C3. Thus, N2 counts 4 non-'X' neighbors. So, N2 = 4.
- N3 (Cell R4, C3): Its neighbors are R3C2 (X), R3C3 (6), R3C4 (X), R4C2 (N2), and R4C4 (N4). The non-'X' neighbors are R3C3, R4C2, and R4C4. Thus, N3 counts 3 non-'X' neighbors. So, N3 = 3.
- N4 (Cell R4, C4): Its neighbors are R3C3 (6), R3C4 (X), and R4C3 (N3). The non-'X' neighbors are R3C3 and R4C3. Thus, N4 counts 2 non-'X' neighbors. So, N4 = 2.
Final Sum Calculation
The values calculated for the last row are N1=2, N2=4, N3=3, and N4=2.
The sum of these four numbers is calculated as:
Sum = N1 + N2 + N3 + N4
Sum = 2 + 4 + 3 + 2
Sum = 11
Important Questions from Puzzles
- 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 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.
