Category: Brain Teasers

A collection of Math, Chess, Detective, Lateral, Insight, Science, Practical, and Deduction puzzles, carefully curated by Puzzle Prime.

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Lost In the Forest

Section: Brain Teasers Category: Mathematics
Difficulty: Tags: ,

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?

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:

  1. 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.
  2. 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.
  3. 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.
  4. Keep walking straight for 100 meters until you reach point D on the tangent t.
Unknown Author September 22, 2023
2 Comments

An Ant’s Path

Section: Brain Teasers Category: Mathematics
Difficulty:

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?

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 √2.

Unknown Author September 19, 2023
2 Comments

A Square and an Invisible Point

Section: Brain Teasers Category: Mathematics
Difficulty:

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?

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
0 Comments

Touch or Don’t Touch

Section: Brain Teasers Category: Practical
Difficulty:

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”?

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
2 Comments

Five Points, Ten Distances

Section: Brain Teasers Category: Deduction
Difficulty:

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?

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:

  1. AB = 5, BC = 6, CD = 9, DE = 2
  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
1 Comment

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