Brain Teasers 5 - Puzzle Prime

A String Around a Rod

Section: Brain Teasers Category: Mathematics

Difficulty: Medium Tags: Geometry

A string is wound around a circular rod with circumference 10 cm and length 30 cm. If the string goes around the rod exactly 4 times, what is its length?

SOLUTION

Imagine the circular rod is actually a paper roll and the string is embedded inside the paper. When we unroll it, we get a paper rectangle 30cm×40cm with the string embedded along the diagonal. Using the Pythagorean theorem, we find that the length of the string is 50cm.

Unknown Author October 7, 2023

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Imprisoned Logicians

Section: Brain Teasers Category: Deduction

Difficulty: Expert Tags: Featured

Two friends, logicians – Ein and Stein – get imprisoned in two distant cells in a castle. Both cells have just one door, and a window with 8 bars in the first cell, and 12 bars in the second cell. The first day both logicians get the same letter from the prison master:

“The total number of bars in the two prison cells in this castle is either 18 or 20. Starting tomorrow, every morning I will go first to Ein and then to Stein, and will ask how many bars the other logician has. If one of you answers correctly, I will immediately let both of you leave the castle. If one of you answers incorrectly, I will execute both of you. Of course, you can always decide not to answer and just stay imprisoned.
I have sent a copy of this letter to you and your friend. There is no point in trying to communicate with him – your cells are far away from each other, and he won’t hear you.”

Will the logicians manage to escape the castle eventually? When will they do it?

SOLUTION

Solution coming soon.

Unknown Author October 1, 2023

8 Comments

Get One Hundred

Section: Brain Teasers Category: Deduction

Difficulty: Advanced

9 8 7 6 5 4 3 2 1 = 1 0 0

Add 3 pluses and 1 minus (not necessarily in that order) anywhere above in order to get a valid equality.

SOLUTION

The answer is:

9 8-7 6+5 4+3+2 1 = 1 0 0

Unknown Author September 28, 2023

2 Comments

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Lost In the Forest

Section: Brain Teasers Category: Mathematics

Difficulty: Expert Tags: Featured, Geometry

You are lost in the middle of a forest, and you know there is a straight road exactly 1 km away from you, but not in which direction. Can you find a path of distance less than 640 m which will guarantee you to find the road?

SOLUTION

Imagine there is a circle with a radius of 100 m around you, and you are at its center O. Let the tangent to the circle directly ahead of you be t. Then, follow the path:

Turn left 30 degrees and keep walking until you reach the tangent t at point A for a total of 100×2√3/3 meters, which is less than 115.5 meters.
Turn left 120 degrees and keep walking along the tangent to the circle until you reach the circle at point B for a total of 100×√3/3 which is less than 58 meters.
Keep walking around the circle along an arc of 210 degrees until you reach point C for a total of 100×7π/6 which is less than 366.5 meters.
Keep walking straight for 100 meters until you reach point D on the tangent t.

Unknown Author September 22, 2023

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An Ant’s Path

Section: Brain Teasers Category: Mathematics

Difficulty: Medium

An ant is positioned at one of the vertices of a cube and wants to get to the opposite vertex. If the edges of the die have length 1, what is the shortest distance the ant needs to travel?

SOLUTION

We unfold a cube to get a cross-shaped figure. Then, the problem is to find the shortest path between two points separated by a horizontal distance of 2 units and a vertical distance of 1 unit.

It is easy to see that the path in question is the one passing through the middle of the edge between the start and end points, and which has a distance of √5.

Unknown Author September 19, 2023

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Kings and Queens

Section: Brain Teasers Category: Insight

Difficulty: Expert Tags: Featured

What should follow the sequence of diagrams shown below?

SOLUTION

The diagrams represent consecutive monarchs of England:

King Edward the 8-th → Ke8
King George 6-th → Kg6
Queen Elizabeth 2-nd → Qe2

Therefore, the next diagram should represent King Charles the 3-rd → Kc3.

Only Connect September 13, 2023

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A Square and an Invisible Point

Section: Brain Teasers Category: Mathematics

Difficulty: Medium

There is a square drawn on a piece of paper and also a point marked with invisible ink. You are allowed to draw 3 lines on the paper and for each of them you will be told whether the point is on its left, on its right, or lies on the line. Your task is to find out whether the point is inside the square, outside the square, or on its boundary. How do you do it?

SOLUTION

Draw one of the diagonals of the square. Then, draw the 2 lines containing the sides of the square that are on the same side as the invisible point.

Unknown Author September 10, 2023

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The Hardest Mate in 2

Section: Brain Teasers Category: Chess

Difficulty: Hard

White to play and mate in 2.

Note: Magnus Carlsen spent almost 2 minutes solving this puzzle.

SOLUTION

The first move is 1. Qa8. If Black plays Qd4, then White responds with Re3#. Otherwise, White plays either Nc5# or Nd6#, so that Black cannot capture the Knight neither with the Rook or the Queen.

Unknown Author September 4, 2023

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Touch or Don’t Touch

Section: Brain Teasers Category: Practical

Difficulty: Hard

For this puzzle/game, you need to keep presenting various words to your friends and telling them whether they are “TOUCH” or they are “DON’T TOUCH”. Below, we have listed several words from each category.

TOUCH: banana, proof, mouse, keyboard, promo, woman

DON’T TOUCH: cherry, solution, cat, screen, discount, girl

Can you guess what determines whether a word is “TOUCH” or “DON’T TOUCH”?

SOLUTION

Words that make your lips touch when pronounced belong to the “TOUCH” category, while the others belong to the “DON’T TOUCH” category. The sounds “P”, “B”, “M”, and “W” that cause this are called “bilabial”.

Unknown Author September 1, 2023

3 Comments

Five Points, Ten Distances

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Five points, A, B, C, D, and E, lie on a line. The distances between them in ascending order are: 2, 5, 6, 8, 9, X, 15, 17, 20, and 22. What is X?

SOLUTION

We assume that the points are ordered A to E from left to right. We have AE = 22 and either AD = 20, BE = 17, or AD = 17, BE = 20. Without loss of generality AD = 20, BE = 17, and therefore AB = 5, BD = 15, DE = 2. The distance of 6 is associated with either BC or CD, and therefore the points are arranged in one of these two ways:

AB = 5, BC = 6, CD = 9, DE = 2
AB = 5, BC = 9, CD = 6, DE = 2

If it is the latter, we get the sequence of distances: 2, 5, 6, 9, 11, 14, 15, 17, 20, 22, which does not fit the provided sequence.

If it is the former, we get the sequence of distances: 2, 5, 6, 8, 9, 14, 15, 17, 20, 22, and therefore X = 14.

Unknown Author August 28, 2023

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