Brain Teasers 52 - Puzzle Prime

Chess Cylinder

Section: Brain Teasers Category: Chess

Difficulty: Medium

Imagine the following game occurs on a cylindrical board, on which the a-file and h-file are attached to each other. White plays first and mates Black in 2 moves.

SOLUTION

White plays Rook on a5, then Ra1#. He can’t take the pawn on a6, because Black will take back with the pawn on h7.

Unknown Author September 1, 2017

2 Comments

Half Empty, Half Full

Section: Brain Teasers Category: Insight

Difficulty: Advanced

You have a glass with perfectly cylindrical shape which has some water in it. How can you figure out if the glass is exactly half full without using any measurement tools (like a ruler)?

SOLUTION

Use the geometry of the cylinder. Start tilting the glass until the water surface gets either to the top or the bottom edge. If the glass is exactly half full, then the surface should touch both edges simultaneously.

Unknown Author August 28, 2017

1 Comment

Single Word

Section: Brain Teasers Category: Insight

Difficulty: Advanced

Cross out nine letters so that the remaining letters spell a single word.

N A I S N I E N L G E L T E T W E O R R S D

SOLUTION

Cross out every other letter starting with the first one – N I N E L E T T E R S.

The remaining letters are – A S I N G L E W O R D.

Unknown Author August 22, 2017

2 Comments

Sarah’s Mother

Section: Brain Teasers Category: Insight

Difficulty: Medium

If Sarah’s mother is Barbara, then Barbara is the ??? of Sarah’s mother.

SOLUTION

The answer is NAME.

Puzzle Prime August 19, 2017

0 Comments

Policeman and Thief

Section: Brain Teasers Category: Mathematics

Difficulty: Expert

A town consists of 3 horizontal and 3 vertical roads, separated by 4 square blocks. A policeman and a thief are running along the roads with speeds of 21km/h and 10km/h respectively. Show that the policeman has a strategy ensuring he will eventually see the thief.

Remark: The policeman can see the thief if they are on the same road at some moment. He has no idea about his position at any time.

SOLUTION

A working strategy for the policeman would be to go to the center and to start encompassing the four blocks clock-wise one by one, in a clockwise manner.

Since the policeman is twice as fast as the thief if the thief is in the center of the town at some point, then there exists a moment in which the policeman is in the center, and the thief is not on the boundary, i.e. he gets shot.

Now, assuming the thief never visits the center, his angle with respect to the coordinate system defined by the two middle roads changes continuously. The angle of the policeman with respect to the same coordinate system can be defined to change continuously as well. Since the policeman needs less time to increase his angle with 360 degrees than the thief, there will be a moment when the two have the same angle. However, this implies that the policeman will be able to see the thief and shoot him.

Unknown Author August 16, 2017

0 Comments

Cork in a Glass

Section: Brain Teasers Category: Science

Difficulty: Hard

You have a jar filled with water and a glass. If you pour some water into the glass and place a cork in it, the cork will float towards the edges of the glass. What is the easiest way to make the cork float towards the center?

SOLUTION

Since the liquid molecules adhere to the glass molecules on the sides of the glass, the water level there is higher and buoyancy makes the cork float in that direction. If you fill the glass all the way to the edge, then the water surface will be convex and the cork will float towards the center.

Unknown Author August 7, 2017

0 Comments

Lucky Day

Section: Brain Teasers Category: Insight

Difficulty: Easy

Scientists have discovered that on one particular date in the year, there is a significantly smaller number of people who die. Do you know which one?

SOLUTION

February 29 – it happens only once every four years.

Unknown Author August 1, 2017

0 Comments

Picture from Russia

Section: Brain Teasers Category: Detective

Difficulty: Advanced

Look at the picture below and answer the following questions:

What time of the day is it?
Is it early spring or a late fall?
Is the river navigable?
Which direction does the river flow? (North, East, South or West?)
Is the river deep or shallow at the side where the boat is?
Is there a bridge across the river nearby?
How far is the railroad from here?
Do the birds fly North or South?

SOLUTION

2. People are sowing the crops, so it is early spring.
8. Since it is spring, birds are flying North.
1. Since birds are flying North, the shadows are pointing East, and therefore it is morning.
4. Judging by the water around the buoy, the river is flowing South.
3. Since there is a buoy, the river must be navigable.
5. The fishing line is long, so the river must be deep.
6. There would not be a ferry if there was a bridge nearby.
7. The guy on the left looks like a railroad worker, so probably the railroad is nearby.

Unknown Author July 28, 2017

4 Comments

Knocked Off Piece

Section: Brain Teasers Category: Chess

Difficulty: Expert

The following position occurs in a real game, right after one of the pieces gets knocked off the board. What was the piece?

SOLUTION

It was a black knight. First, notice that the black pawns have moved 14 times diagonally and thus they have taken 14 pieces. Therefore the knocked off piece is black. Since it is impossible for both kings to be checked at the same time, the missing piece was positioned on a2. It couldn’t be a queen or a rook, because the white king would be checked both by it and the pawn on b3, which is impossible. Therefore the missing piece is either the black white-squared bishop or the black knight. However, the pawns on b7 and d7 haven’t been moved the entire game and then the black white-squared bishop hasn’t either. Thus we conclude that the knocked off piece is a black knight.

Unknown Author July 19, 2017

0 Comments

Tetris Puzzle

Section: Brain Teasers Category: Mathematics

Difficulty: Advanced

As a birthday present last year, I received some fridge magnets. They didn’t come as a puzzle, so I don’t know if they have a solution, but I made a puzzle out of them anyway. The magnets are tetrominoes. There are 7 of each shape. Is it possible to arrange them into a 7×28 rectangle so that they are all used and all inside the rectangle? The closest I have managed is this:

SOLUTION

No, it is impossible. Imagine you are placing the tetrominoes on a 7×28 chess board. All of them, except for the T-shaped ones cover exactly 2 black and 2 white cells. Each of the T-shaped tetrominos covers either 2 more black cells than white cells or 2 more white cells than black cells. Since there are 7 of them, combined they will cover either more black cells than white cells or more white cells than black cells. Therefore all pieces on the picture can not cover perfectly a rectangle, which contains an equal number of black and white cells.

Source:

Puzzling StackExchange

James Webster July 16, 2017

0 Comments