Suppose a n × n chessboard is missing two opposite corners. Prove that no matter what n is, you will not be able to cover the remaining squares exactly with dominoes.

Q: Suppose that I want to purchase a tablet computer. I can choose either a large or a small screen; a…

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Q: What does Chebyshev’s theorem with k=12 tells us about the number of heads that we may get in 900…

A: Given K=12

Q: If I have 3,493 points, right now, and I get 320 points every day, and I want to get 27,650 points,…

A: We have to find number of months to achieve 27650 points.

Q: A combination lock uses 3 numbers, each of which can be 0 to 23. If there are no restrictions on the…

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Q: A witness to a hit-and-run accident tells the police that the license plate of the car in the…

A: There are 26 letters and 10 digits. The first letter is A. So 1 choice for the first letter. For the…

Q: How many independent variables are there in a 10 x 2 x 6 x 2 factorial design?

A: Independent variables in 10×2×6×2.

Q: Bonita purchases 1225 white bouncy​ balls, 952yellow bouncy​ balls, and 504 orange bouncy balls. He…

A: Find the H.C.F of 1225, 952 and 504 that is 7 no of bags we have.

Q: (i) Determine how many rows are in the corner section of a stadium containing 3920 seats if the…

A: the total number of seats in the stadium are 3920  the first row has 10 seats,  The second row has…

Q: If a chicken and one half lays an egg and one half in a day and one half, how may eggs will 30…

A: According to the provided information, 1.5 chicken lays 1.5 egg in 1.5 days.That is, 1.5 eggs = 1.5…

Q: A person is 4 years old and his sister is half his age, so if this person is a hundred years old,…

A: Given: Age of the person = 4 years Age of the sister = 2 years (half of that of person's age)…

Q: How many diagonals can you draw from one vertex in polygon with 35 sides

A: Given data: The given numbers of sides of the polygon are n=35. The expression for the numbers of…

Q: A cube of 5 cm is painted on all its faces .If it is sliced into 1 cubic centimetre cubes , how many…

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Q: How many squares (of all sizes) are there on a standard 8x8 Chess board?

A: we have to find  how many squares of all sizes in 8*8 chess board ;

Q: A fast food restaurant advertises that it offers any combination of 8 condiments on a hamburger,…

A: The number is obtained as follows: The number of choosing none of the condiments on a hamburger:…

Q: Two boxes, A and B, contain 2 balls and 6 white, and B contains 2 red and white. If one of the boxes…

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Q: If a men working 6hours a day can do a work in 88days, then 6men working 8hours a day can do it in…

A: Given that men working 6 hours a day can do work in 88 days

Q: If there are 12 teams in a basketball tournament and each team must play every other team in the…

A: The given question requires number of pairs between two teams. Note that if team A and team B are…

Q: Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 80% of their games.…

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Q: A sum of $1300 is divided amongst P,Q,R and S such that P share/Q share = Q share / R share=R…

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Q: Suppose you're on a 4 x 6 grid, and want to from the bottom left to the top right. How many…

A: That is, go all the way right (6 right's), then all the way up (4 up's) into the 4*6 grid because i…

Q: A combination lock uses 3 numbers, each of which can be 0 to 33. If there are no restrictions on the…

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Q: B. At least how many moves are needed to solve the Tower of Hanoi problem with 4 chips, 5 chips and…

A: Given : Tower of Hanoi problem with 4 chips, 5 chips and 6 chips

Q: In a stack of cards, each card has a number and letter on opposite sides. You are told that all…

A: Each card has a number and a letter on opposite sides. Any number that is even as well as divisible…

Q: In the United States, telephone numbers consist of a three-digit area code followed by a seven-digit…

A: Given problem Given that   In the United States, telephone numbers consist of a three-digit area…

Q: Suppose that the number of students in a class increase by 2, the number of ways they may be…

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Q: A checker is placed in the bottom row of a checker board as shown below. It can move diagonally…

A: This is a counting problem.. we will solve it using the approach of dynamic programming

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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Q: In a medical supply​ room, there are 165 packages of type O positive blood and 210 packages of type…

A: Given Information - Number of type O positive blood packages = 165 Number of type AB negative blood…

Q: In row 2 there are 28 seats and in row 4 there are 44 seats. What is the number of seats in row 10?

A: The given data in the question is converted into a table

Q: A combination lock uses 3 numbers, each of which can be 0 to 38. If there are no restrictions on the…

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Q: The Japanese game called Chu Shogi uses a square board. The board is covered with smaller squares…

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Q: Two integers, a and b, have a product of 48. What is the least possible sum of a and b? The least…

A: Answer is a+b= -49. Explanation is given below...

Q: If Alice is tall, Bob is taller than her, and Carol is taller than both of them, then Carol is tall.

A: Given that Bob is taller than Alice, So Bob>Alice    (1) Carol is taller that Alice and Bob. It…

Q: In a league of nine football teams, each team plays every other team in the league exactly once. How…

A: Given football league consisting of 9 teams, each team play each other team exactly once

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

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Q: If Snoopy danced a jig, then Charles Schultz did not write a sonata.

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Q: In the Brady's Family, each girl has twice as many brothers as she has sisters. However, each boy…

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Q: A witness to a hit-and-run accident tells the police that the license plate of the car in the…

A: From the given information, There are 26 letters in total in which we have to select three letters…

Q: Is it possible to plant 10 trees in 10 straight rows with 3 trees in each row? Hint: Desargues says…

A:

Q: Suppose two squares of the same color are removed from an 8 x 8 chessboard. Is it possible to tile…

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Q: Is it possible for two numbers to have the same least common multiple and greatest common devisor?

A: To check whether for two numbers can have the same LCM and HCF.

Q: If the sum of the digits is divisible by 2, then the number is divisible by 2. true or false

A: If the sum of the digits is divisible by 2, then the number is divisible by 2.

Q: Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 60% of their games.…

A: Given.... Bob and Doug play a lot of Ping-Pong, but Doug is a much better player, and wins 60% of…

Q: In the United States, telephone numbers consist of a three-digit area code followed by a seven digit…

A:

Q: In the United States, telephone numbers consist of a three-digit area code followed by a seven-digit…

A: Given problem Given that   In the United States, telephone numbers consist of a three-digit area…

Q: two diagonally opposite corners of a standard chessboard are removed. Is it possible to cover the…

A: Given that, Two diagonally opposite corners of a standard chessboard are removed. Every domino in a…

Q: Show that a 6 × n board (n ≥ 2) can be tiled with L-shaped tiles, without gap and overlapping. Each…

A: Before we begin proving the statement, we shall understand the shapes. An L-shaped three-square tile…