Puzzles 47 - Puzzle Prime

Wobbling Table

Section: Brain Teasers Category: Mathematics

Difficulty: Hard

A perfectly symmetrical square 4-legged table is standing in a room with a continuous but uneven floor. Is it always possible to position the table in such a way that it doesn’t wobble, i.e. all four legs are touching the floor?

SOLUTION

The answer is yes. Let the feet of the table clockwise are labeled with 1, 2, 3, 4 clockwise. Place the table in the room such that 3 of its feet – say 1, 2, 3, touch the ground. If foot 4 is on the ground, then the problem is solved. Otherwise, it is easy to see that we can not put it there if we keep legs 2 and 3 in the same places. Now start rotating the table clockwise, keeping feet 1, 2 and 3 on the ground at all times. If at some point foot 4 touches the ground as well, the problem is solved. Otherwise, continue rotating until foot 1 goes to the place where foot 2 was and foot 2 goes to the place where foot 3 was. Foot 3 will be on the ground, but this contradicts the observation that initially we couldn’t place legs 2, 3 and 4 on the ground without replacing feet 2 and 3.

Unknown Author December 25, 2019

0 Comments

Prank the Professors

Section: Brain Teasers Category: Deduction

Difficulty: Medium

Three professors fell asleep under a tree. At some point a prankster passed by and painted their faces with black dye. When the professors woke up, each of them saw the others’ faces and started laughing at them. After a while though, they stopped laughing, realizing that their own faces were painted as well. How did they deduce that?

SOLUTION

Let us denote the professors with A, B and C. The thought process of A would go like this: “If my face is not painted, then B will see that C is laughing at him and will realize immediately that he is being pranked. However, B was laughing for a while and therefore my I must being pranked as well.”. Then A will stop laughing and the same will happen with the other two professors B and C.

Unknown Author December 22, 2019

0 Comments

FEATURED

Repetitive

Section: Brain Teasers Category: Insight

Difficulty: Advanced Tags: Featured, Words

You have two groups of words:

black, word, English, brief, noun, grandiloquent, last
white, number, Russian, long, verb, unpretentious, first

To which group does “repetitive” belong?

SOLUTION

The first group contains self-explanatory words (known as autologicals), the second group does not. Therefore “repetitive” should belong to the first group.

Puzzle Prime December 19, 2019

0 Comments

Young, Middle-Aged, Old

Section: Casual Puzzles Category: Riddle

Difficulty: Easy

When young, I am sweet in the sun.
When middle-aged, I make you gay.
When old, I am valued more than ever.

What am I?

SOLUTION

The answer is WINE.

Unknown Author December 16, 2019

2 Comments

Chocolate Bar

Section: Brain Teasers Category: Insight

Difficulty: Medium

Louis has a bar of chocolate 4×6 which is marked into 24 little squares. At each step, he breaks up one of its pieces along any of the marked horizontal/vertical lines. Show that no matter how he does that, it will always take the same number of steps until the chocolate is broken into single 1×1 pieces.

SOLUTION

Every time he splits the chocolate, the number of pieces increases by 1. Therefore it will always take him 23 steps to split it into single pieces.

Unknown Author December 13, 2019

0 Comments

Llama Lawn

Section: Casual Puzzles Category: Maze

Difficulty: Medium

Get from START to END in this maze, created by Sean Jackson.

SOLUTION

The solution is shown below.

Sean Jackson December 10, 2019

0 Comments

Four Points in the Plane

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced Tags: Geometry

Find all configurations of four points in the plane, such that the pairwise distances between the points take at most two different values.

SOLUTION

All 6 configurations are shown below: a square, a rhombus with 60°-120°-60°-120°, an equilateral triangle with its center, an isosceles triangle with 75°-75°-30° and its center, a quadrilateral with 75°-150°-75°-150°, and a trapezoid with base angles of 72°.

Unknown Author December 7, 2019

2 Comments

Guess the Fruits

Section: Brain Teasers Category: Deduction

Difficulty: Medium

You are given 3 boxes – one labeled “Apples”, one labeled “Bananas”, and one labeled “Apples and Bananas”. You are told that the labels on the boxes have been completely mismatched, i.e. none of the three labels is put on its correct box. How can you open just one box and pick a random fruit from it, so that after seeing the fruit, you can guess correctly the contents of every box out of the three?

SOLUTION

Open the box labeled “Apples and Bananas”. If you pick a banana from it, then the box labeled “Bananas” will contain apples, and therefore the box labeled “Apples” will contain apples and bananas. Similarly, if you pick an apple from it, then the box labeled “Apples” will contain bananas, and therefore the box labeled “Bananas” will contain apples and bananas”.

Unknown Author December 4, 2019

0 Comments

Thank You!

Section: Brain Teasers Category: Lateral

Difficulty: Hard

A cowboy walks into a bar and asks the barman for a glass of water. The barman pulls out a gun instead and points it at the man. The man genuinely says “Thank you” and walks out.

What happened?

SOLUTION

The cowboy had hiccups and needed water. The barman shocked him with his gun instead and that cured the hiccups.

Unknown Author December 1, 2019

0 Comments

Twiddled Bolts

Section: Brain Teasers Category: Insight

Difficulty: Advanced

Two identical bolts are placed together so their grooves intermesh. If you move the bolts around each other as you would twiddle your thumbs, holding each bolt firmly by the head so it does not rotate and twiddling them in the direction shown below, will the heads:

(a) move inward
(b) move outward, or
(c) remain the same distance from each other?

SOLUTION

One of the bolts will be screwing itself, and the other one will be unscrewing itself. This will happen at the same pace and the bolts will remain the same distance from each other. Thus the answer is (c).

Martin Gardner November 28, 2019

0 Comments