Difficulty: Advanced

 

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Picture from Russia

Section: Brain Teasers Category: Detective
Difficulty:

Look at the picture below and answer the following questions:

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

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.

puzzle
Unknown Author July 28, 2017
4 Comments

Tetris Puzzle

Section: Brain Teasers Category: Mathematics
Difficulty:

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:

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

puzzle
James Webster July 16, 2017
0 Comments

Camel in the Desert

Section: Brain Teasers Category: Insight
Difficulty:

One man is trying to cross the desert to reach the neighboring village. It takes 4 days to get there, but his camel can carry bananas which will feed him for 3 days only. How can the man reach the neighboring village without starving?

The man travels one day, leaves one portion of bananas in the desert and returns back to his village. Then he leaves again with 3 new portions of bananas, picks the portion left in the desert on his way and ends up in the neighboring village on the sixth day.

puzzle
Unknown Author June 19, 2017
5 Comments

Three Voting Prisoners

Section: Brain Teasers Category: Insight
Difficulty:

Each night one of three prisoners has steak for dinner, while the other two have fish tacos. Also every night, each of the three prisoners votes for one of the following two options:

  1. All of us have had steak at least once.
  2. Don’t know yet.

If a majority go with option 2, nothing happens that night. If a majority go with option 1, then they are set free if they are right and executed if they are wrong. The distribution of votes is kept secret, so it is unknown what each of the others voted. Also, it is known that every prisoner eventually will get a steak.

The three prisoners can have a brief strategy meeting and after that, they are not allowed to communicate.  What should the prisoners’ strategy be?

The prisoner who gets a steak the first night should always vote 2, whereas the other two prisoners should vote 2 until the night they get a steak, and 1 every night after.

Source:

Puzzling StackExchange

puzzle
Tyler Seacrest June 1, 2017
3 Comments

Non-Negative

Section: Brain Teasers Category: Mathematics
Difficulty:

You have a rectangular grid and arbitrary real numbers in its cells. You are allowed repeatedly to multiply the elements in any row or any column by -1. Prove that you can make all row sums and all column sums non-negative simultaneously.

If there is any row or column in the grid with a negative sum, multiply it by -1. Since on every step the total sum of the numbers in the grid increases, we will be able to do this procedure only finitely many times. In the end, all row sums and column sums will be non-negative.

puzzle
Unknown Author May 10, 2017
0 Comments

Seven Bridges

Section: Brain Teasers Category: Insight
Difficulty:

This is a map of old-time Kongsberg. The green shapes are bridges which connect the different parts of the city. Can you find a path through the city which goes through every bridge exactly once?

No, you cannot. Notice that, except for the first city and the last city section you finish, the number of bridges used in every other section is even. However, there are three sections with an odd number of bridges, and therefore you cannot use all bridges exactly once.

puzzle
Unknown Author March 19, 2017
0 Comments

Missing Pawns

Section: Brain Teasers Category: Chess
Difficulty:

White to play and mate in 4 moves.

Remark: The position on the diagram is one which occurs in actual play.

Notice that the black queen and the black king have switched positions. However, this can happen only if some pawns have been moved. Therefore, we can conclude that the bottom row on the diagram is actually the 8th row of the chessboard. All black and all white pieces have reached their respective opposite sides of the board.

Now, White’s first move is Kb8-d7. The only moves black can play are with the knights. If Black plays Kb1-a3, Kb1-c3 or Kg1-h3, white mates in 2 more moves – Kd7-c5 and Kc5-d3. If Black moves Kg1-f3, then after Kd7-c5 Black can delay the mate by playing Kf3-e5. However, after the white queen takes it with Qxe5, Kc5-d3 is unavoidable.

puzzle
Unknown Author February 19, 2017
2 Comments

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