Difficulty: Advanced

 

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We Go on Vacation

Section: Brain Teasers Category: Practical
Difficulty:

For this puzzle/game, you will need to find a group of friends, preferably 5 or more. The premise is that you will go together on a vacation but each of you can bring only specific items there. The rules regarding which items can be brought and which not are known by one of the players and the other ones are trying to guess them.

In the exchange below, George is the one organizing the trip and the one who knows which items the rest are allowed to bring.

GEORGE: I will take my guitar with me. What do you want to take?

SAM: Can I take an umbrella with me?

GEORGE: No, you cannot take an umbrella, but you can take some sunscreen.

HELLEN: Can I take a scarf with me?

GEORGE: No, you cannot take a scarf, but you can take a hat.

MONICA: Can I take a dress with me?

GEORGE: No, you cannot take a dress, but you can take some makeup.

Can you guess what the rules of the game are?

Everyone is allowed to take with themselves only items whose first letter is the same as the first letter of their names. Thus, George can take a Guitar, Sam can take Sunscreen, Hellen can take a Hat, and Monica can take Makeup.

puzzle
Unknown Author December 22, 2022
0 Comments

The Die Game

Section: Brain Teasers Category: Mathematics
Difficulty: Tags:

You pick a number between 1 and 6 and keep throwing a die until you get it. Does it matter which number you pick for maximizing the total sum of the numbers in the resulting sequence?

In the example below, the picked number is 6 and the total sum of the numbers in the resulting sequence is 35.

No matter what number you pick, the expected value of each throw is the average of the numbers from 1 to 6 which is 3.5. The choice of the number also does not affect the odds for the number of throws until the game ends, which is 6. Therefore, the total sum is always 3.5 × 6 = 21 on average, regardless of the chosen number.

puzzle
Unknown Author December 7, 2022
7 Comments

Annihilating Matrix

Section: Brain Teasers Category: Mathematics
Difficulty:

The numbers 1, 2, … , 100 are arranged in a 10×10 table in increasing order, row by row and column by column, as shown below. The signs of 50 of these numbers are flipped, such that each row and each column have exactly 5 positive and 5 negative numbers. Prove that the sum of all numbers in the resulting table is equal to 0.

Represent the initial table as the sum of the following two tables:

Since the sum of the numbers in each row of the first table is equal to 0 and the sum of the numbers in each column of the second table is equal to 0, it follows that the sum of all numbers in both tables is equal to 0 as well.

Source:

Quantum Magazine, November-December 1991

puzzle
S. Ageyev September 28, 2022
0 Comments

Math Homework

Section: Brain Teasers Category: Mathematics
Difficulty:

A student was given math homework consisting of the following three problems. What is so special about this homework?

  1. What would the value of 190 in hexadecimal be?
  2. Twenty-nine is a prime example of what kind of number?
  3. At time t = 0, water begins pouring into an empty tank so that the volume of water is changing at a rate V’(t)=sec²(t). For time t = k, where 0 < k < π/2, determine the amount of water in the tank.

The answer to each of the problems in the homework is hidden within the question itself:

  1. What would the value of 190 in hexadecimal be?
    The answer is be.
  2. Twenty-nine is a prime example of what kind of number?
    The answer is prime.
  3. At time t = 0, water begins pouring into an empty tank so that the volume of water is changing at a rate V’(t)=sec²(t). For time t = k, where 0 < k < π / 2, determine the amount of water in the tank.
    The answer is tank.
Source:

Math Horizons, MAA

puzzle
Raymond Greenwell, Head-Royce School Math Club and Rheta Rubenstein September 19, 2022
0 Comments

More Sisters on Average

Section: Brain Teasers Category: Mathematics
Difficulty:

Who have more sisters on average in a society: boys, girls, or is it equal?

Remark: Assume that each child is born a boy or a girl with equal probability, independent of its siblings.

The average number of sisters is roughly the same for both boys and girls. To see this, notice that every girl in every family contributes “one sister” to each of its siblings who are either a boy or a girl with equal probability. Therefore, every girl contributes on average the same number of sisters to the group of boys and to the group of girls. Since there is roughly the same number of boys and girls in the society, the average number of sisters for boys and girls is the same.

puzzle
Unknown Author September 1, 2022
0 Comments

Send More Money

Section: Brain Teasers Category: Mathematics
Difficulty: Tags:

Replace every letter with a different digit between 0 and 9, such that you get a correct calculation.

The answer is 9567 + 1085 = 10652.

You can first see that M = 1. Then S = 8 or 9 and O = 0. MORE is at most 1098, and if S = 8, then E = 9, N is either 9 or 0, but this is impossible. Therefore S = 9, N = E + 1. You can check easily the 6 possibilities for (N, E) and then find the answer.

puzzle
Henry Dudeney August 10, 2022
1 Comment

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