Advanced – Puzzle Prime

Airplane on a Conveyor Belt

Section: Brain Teasers Category: Science

Difficulty: Advanced

A Boeing 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Will the plane take off?

SOLUTION

Solution coming soon.

Unknown Author March 19, 2024

2 Comments

Had Had Had Had Had

Section: Brain Teasers Category: Deduction

Difficulty: Advanced Tags: Words

A teacher in English had asked James and John to describe a man who had suffered from a cold in the past. James while John had had had had had had had had had had had a better effect on the teacher.

Add punctuation to the sentence in bold, so that it makes sense.

SOLUTION

A teacher in English had asked James and John to describe a man who had suffered from a cold in the past. James, while John had had “had”, had had “had had”; “had had” had had a better effect on the teacher.

The meaning is that John had used the phrase “had a cold”, whereas James had used the phrase “had had a cold”. The former, being more grammatical, had resulted in a better impression on the teacher.

Unknown Author March 16, 2024

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Fold Into a Cube

Section: Brain Teasers Category: Practical

Difficulty: Advanced

Cut out the black shape and then fold it perfectly into a cube, without overlapping.

SOLUTION

If the size of each of the small edges of the shape is equal to 1cm, then its area is equal to 30cm². Thus, the cube that is formed by the shape must have an edge of length √5cm. If we set the center of the black shape to be the center of one of the cube’s faces, then the four closest vertices must lie on the boundary of the shape, √2.5cm away. This determines uniquely the folding of the shape which is shown on the simulation below.

Source:

Puzzling Stackexchange

plasticinsect March 13, 2024

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Average Salary

Section: Brain Teasers Category: Insight

Difficulty: Advanced

Three friends, A, B and C, want to find out what their average salary is without disclosing their own salaries to the others. How can they do it using only verbal communication?

SOLUTION

A tells B some number, then B adds his salary to it and tells the result to C, then C adds his salary and tells the result to A. Now A subtracts the number he told B in the beginning, adds his own salary and divides by 3. Repeat the same procedure with B and C starting first.

Unknown Author March 10, 2024

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Three Inch Origami

Section: Brain Teasers Category: Insight

Difficulty: Advanced

What is the minimum number of folds you need in order to create a 3-inch measurement from an 8.5×11 inches paper?

SOLUTION

You need just 2 folds, as shown on the picture below.

Source:

Puzzling StackExchange

DEEM February 25, 2024

0 Comments

Protect the Treasure

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced

Nine pirates have captured a treasure chest. In order to protect it, they decide to lock it using multiple locks and distribute several keys for each of these locks among them, so that the chest can be opened only by a majority of the pirates. What is the minimum number of keys each of the pirates should get?

SOLUTION

First, we show that for every four pirates, there exists a lock which cannot be opened only by them and can be opened by everyone else. We choose an arbitrary group of four pirates. If they can open every lock, then they can access the treasure without the need of a majority. If any of the remaining pirates cannot open that lock, then he, together with the initial group of four still cannot access the treasure. Thus, the claim is proved and to each group of four pirates we can assign a unique lock. These are $\binom{9}{4}=126$ locks in total. Finally, every pirate should get keys for $\binom{8}{4}=70$ of these locks, one for each group of four additional pirates he can be a group of.

Unknown Author February 19, 2024

2 Comments

Fish Eat Fish

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced Tags: Probability

A hundred fish are swimming along a stream at different velocities. If one fish catches up to another fish, it eats it and continues swimming. What is the expected number of fish that will survive?

SOLUTION

Notice that the N-th fish in the stream survives if and only if it is the fastest among the first N fish. The probability of this event happening is equal to 1/N. Since the expected number of fish that survive is equal to the sum of the survival probabilities for each of them, the answer is 1+1/2+1/3+…+1/N.

For more details on the last claim, consider reading our blog post “How Many Times on Average?”

Unknown Author February 7, 2024

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Mirror Chess

Section: Brain Teasers Category: Chess

Difficulty: Advanced

Bobby and Garry are playing chess. If Garry is playing with the black figures and agrees to mirror every move Bobby makes, what is the minimum number of moves in which Bobby can mate his opponent?

SOLUTION

Bobby can mate Garry in four moves:

1. d4 d5 2. Qd3 Qd6 3. Qh3 Qh6 4. Qxc8

Unknown Author January 25, 2024

4 Comments

FEATURED

The Mansion

Section: Casual Puzzles Category: Maze

Difficulty: Advanced Tags: Featured

Can you find your way through this mansion, by using the information from the security cameras? In order to escape, you must use the correct key and unlock the exit door.

SOLUTION

The solution is shown below.

Johann Sturcz January 16, 2024

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Mountain Hike

Section: Brain Teasers Category: Insight

Difficulty: Advanced

A man decides to climb a mountain. He starts at sunrise from the bottom of the mountain and arrives at the top at sunset. He sleeps there and on the next day he goes back the same way, descending at higher speed. Prove that there is some point of his path, on which the man will be at the same time on both days.

SOLUTION

Imagine a second man who starts climbing from the bottom of the mountain on the second day and following the first hiker’s first day movements. At some point the first and the second hiker will meet each other, and this will be the point you are looking for.

Unknown Author January 7, 2024

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