Cube Wire Frame Minimum Cuts
The problem requires determining the minimum number of cuts needed to construct a cube's wire frame from a single $12 \text{ m}$ wire.
Cube Structure and Wire Length
A cube has 12 edges. Each edge of the cube measures $1 \text{ m}$.
The total wire length needed to form all edges is calculated as: $12 \text{ edges} \times 1 \text{ m/edge} = 12 \text{ m}$ The provided wire is $12 \text{ m}$ long, exactly matching the total length required.
Efficient Wire Utilization Strategy
The goal is to minimize cuts. This can be achieved by bending the wire. A single segment of wire measuring $3 \text{ m}$ can be bent to form three consecutive $1 \text{ m}$ edges of the cube. This requires making bends at the $1 \text{ m}$ and $2 \text{ m}$ points along the $3 \text{ m}$ segment.
Calculating Required Segments and Cuts
To construct the total 12 edges of the cube, using the strategy where each segment forms 3 edges, the number of segments needed is: $\frac{12 \text{ total edges}}{3 \text{ edges per segment}} = 4 \text{ segments}$
To obtain 4 distinct segments from one continuous $12 \text{ m}$ wire, the minimum number of cuts required is: $(\text{Number of segments}) - 1 = 4 - 1 = 3 \text{ cuts}$
Making 3 cuts on the $12 \text{ m}$ wire yields four $3 \text{ m}$ segments. Each $3 \text{ m}$ segment can be bent into three $1 \text{ m}$ edges. Soldering these pieces at the vertices completes the cube frame. Fewer cuts would result in fewer segments, which is insufficient to form all 12 edges.
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
