Hard – Page 8 – Puzzle Prime

Special Transaction

Section: Brain Teasers Category: Insight

Difficulty: Hard

One person went to the store and bought groceries for $13.59 total. He paid with a $100 bill, took his change, and left the store. There was something special about this transaction. What is it?

SOLUTION

The person paid with a $100 bill. The cashier returned him a $50 bill, a $20 bill, a $10 bill, a $5 bill, a $1 bill, a quarter, a dime, a nickel, and a cent. The transaction consisted of exactly one of each (frequently used) denominations.

Unknown Author July 7, 2019

1 Comment

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Two Threes, Two Eights

Section: Brain Teasers Category: Mathematics

Difficulty: Hard Tags: Featured

Use exactly two threes (3) and two eights (8) to get the number 24. You can use multiplication (×), division (÷), addition (+), subtraction (-) signs, and brackets. You can not use any advanced arithmetic operations, such as exponential, factorial, etc.

SOLUTION

The answer is shown below.

8 ÷ (3 – 8 ÷ 3) = 24

Unknown Author July 4, 2019

5 Comments

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Three Daughters

Section: Brain Teasers Category: Deduction

Difficulty: Hard Tags: Featured

Two friend mathematicians meet each after a long time and have the following conversation:

– I have 3 daughters, the product of their ages is 36.
– I can’t figure out how old they are, can you tell me more?
– Sure, the sum of their ages is equal to the number of my house.
– I know your house number, but still can’t figure out the ages of your daughters.
– Also, my eldest daughter is called Monica.
– OK, now I know how old your daughters are.

What ages are the three daughters of the mathematician?

SOLUTION

Using the first clue, we find that there are 8 possibilities:

(1, 1, 36) -> sum 38
(1, 2, 18) -> sum 21
(1, 3, 12) -> sum 16
(1, 4, 9) -> sum 14
(1, 6, 6) -> sum 13
(2, 2, 9) -> sum 13
(2, 3, 6) -> sum 11
(3, 3, 4) -> sum 10

Since the second mathematician couldn’t guess the ages even after the second clue, the sum has to be 13. Therefore the only possible options are (1, 6, 6) and (2, 2, 9). However, the third clue suggests that there is an “eldest” daughter and then the correct answer is 2, 2 and 9.

Unknown Author June 26, 2019

1 Comment

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Prisoners and Hats

Section: Brain Teasers Category: Insight

Difficulty: Hard Tags: Featured

100 prisoners are given the following challenge: They will be taken to a room and will be arranged in a column, such that each of them faces the backs of the prisoners in front. After that, black and red hats will be placed on their heads, and the prisoners will be asked one at a time what is the color of their hat, starting from the one at the back of the column. If a prisoner guesses his color correctly, he is spared; if not – he is executed. If every prisoner can see only the hats of the prisoners in front of him in the line, what strategy should they come up with, so that their losses are minimized?

SOLUTION

There is a strategy which ensures that 99 prisoners are spared and there is 50% chance that one of them is executed. Clearly, one can not do better.

The strategy is as follows: The first prisoner (at the back of the line) counts the number of black hats worn by the prisoners in front. If the number is odd, he says “BLACK”. If the number is even, he says “RED”. Then, the second prisoner counts the black hats in front of him, figures out the color of his own hat, and answers the question.The third prisoner sees the number of black hats in front of him and uses this information, along with what the second prisoner’s hat is, to determine the color of his own hat. The prisoners continue in the same manner until all 99 prisoners in the front guess their hat colors correctly. The chance for survival of the first prisoner is 50%.

Unknown Author June 13, 2019

5 Comments

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Manifold

Section: Brain Teasers Category: Practical

Difficulty: Hard Tags: Featured

Manifold is a brilliant puzzle invented by Jerome Morin-Drouin. Based on the origami principle, the goal of Manifold is to fold the printed paper several times, so that eventually you will end up with a 4 × 4 square which is white on one side and black on the other. The Manifolds here are provided by The Incredible Company and are part of their Manifold game which contains a total of 100 puzzles. Click the images, download them, print them, and solve the puzzles.

Source:

Manifold 2 on Amazon

Jerome Morin-Drouin May 28, 2019

4 Comments

One to Eight

Section: Brain Teasers Category: Practical

Difficulty: Hard

Prepare a piece of paper with dimensions 2×4, then fold it four times to form 8 squares. Write on the squares in the top row the numbers 1, 8, 7, 4, and write on the squares in the bottom row the numbers 2, 3, 6, 5.

Now your task is to fold the piece of paper several times, so that the squares end up on top of each other, with the numbers appearing in ascending order top to bottom, and 1 face up.

Once you do this, try again with numbers 1, 8, 2, 7 on the top row, and 4, 5, 3, 6 on the bottom row.

SOLUTION

Coming soon.

Unknown Author May 22, 2019

1 Comment

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King’s Route

Section: Brain Teasers Category: Insight

Difficulty: Hard Tags: Featured

A chess king starts on one cell of a chessboard and takes a non-intersecting tour, passing through each square once, and ending up on the initial square. Show that the king has made no more than 36 diagonal moves.

SOLUTION

The king must visit the 28 perimeter squares in order; otherwise, he will create a portion of the board which is inaccessible for him. However, he can not travel from one square to a neighboring one using only diagonal moves. Therefore, he must make at least 28 horizontal/vertical moves and at most 64 – 28 = 36 diagonal moves.

Kagen Schaefer May 12, 2019

4 Comments

So many eights!

Section: Brain Teasers Category: Mathematics

Difficulty: Hard

Can you draw uncountable many non-intersecting “8” shapes in the plane (they can be contained in one another)?

SOLUTION

No, you can’t. For each “8” shape you can choose a pair of points with rational coordinates – one in its top loop and one in its bottom loop. Since no two “8” shapes can have the same corresponding pair of rational points, their number should be countable.

Unknown Author April 22, 2019

0 Comments

Enemies in the Parliament

Section: Brain Teasers Category: Mathematics

Difficulty: Hard

In a parliament, there are 100 people, and some of these people are enemies with each other. Show that you can split the people into 2 groups so that each person has at least as many enemies in the opposite group as he has in his own.

SOLUTION

For each split of the people into 2 groups, compute the animosity level of each person by subtracting the number of enemies in the opposite group from the number of enemies in his own group. Then, split the people into 2 groups so that the total animosity level of all of them is as little as possible. If there is a person, who has more enemies in his own group than the opposite one, then by transferring him to the other group, we will reduce the total animosity level of the people and will get a contradiction.

Unknown Author March 25, 2019

3 Comments

The Warden and the Three Doors

Section: Brain Teasers Category: Deduction

Difficulty: Hard

An evil warden holds you as a prisoner but offers you a chance to escape. There are 3 doors A, B, and C. Two of the doors lead to freedom and the third door leads to lifetime imprisonment, but you do not which door is what type. You are allowed to point to a door and ask the warden a single yes-no question. If you point to a door that leads to freedom, the warden does answer your question truthfully. But if you point to the door that leads to imprisonment, the warden answers your question randomly, saying either “YES” or “NO” by chance. Can you figure out a way to escape the prison?

SOLUTION

You can point towards door A and ask whether door B leads to freedom. If the warden says “YES”, then you open door B. It can not lead to imprisonment because this would mean that door A leads to freedom and the warden must have told you the truth. If the warden says “NO”, then you open door C. This is because either the warden lied, and then the imprisonment door is A, or he told you the truth, and then the imprisonment door is B.

Unknown Author March 15, 2019

7 Comments