Cut the Pizza
Cut a circular pizza into 12 congruent slices, such that exactly half of them contain crust.
Remark: We say that a slice contains crust if it shares an arc with the boundary of the pizza (with non-zero measure).
SOLUTION
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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Open or Close
If you turn the handle of the top left gear clockwise, will the box in the bottom right open or close?
SOLUTION
Missing Parenthesis
Insert the missing parentheses into each equation to make it true.
SOLUTION
Source:
“Intermediate Algebra for College Students” by Karl. J. Smith and Patrick J. Boyle
Sunome
The main challenge of a Sunome puzzle is drawing a maze. Numbers surrounding the outside of the maze border give an indication of how the maze is to be constructed. To solve the puzzle you must draw all the walls where they belong and then draw a path from the Start square to the End square.
The walls of the maze are to be drawn on the dotted lines inside the border. A single wall exists either between 2 nodes or a node and the border. The numbers on the top and left of the border tell you how many walls exist on the corresponding lines inside the grid. The numbers on the right and bottom of the border tell you how many walls exist in the corresponding rows and columns. In addition, the following must be true:
- Each puzzle has a unique solution.
- There is only 1 maze path to the End square.
- Every Node must have a wall touching it.
- Walls must trace back to a border.
- If the Start and End squares are adjacent to each other a wall must separate them.
- Start squares may be open on all sides, while End squares must be closed on 3 sides.
- You cannot completely close off any region of the grid.
Examine the first example, then solve the other three puzzles.
SOLUTION
The Gun and the Recording
One day, the police found a man dead inside a hut. In his left hand, he was holding a gun. In his right hand, he had a recording device. When the recording was played, the police heard the man talking about how horrible his life was and how he wanted it to end. The recording ended with a gunshot. The police was about to call it a suicide until a detective pointed out a very important clue. What was it?
SOLUTION
Spot the Robber
The streets of the city are a square grid that extends infinitely in all directions. One of the streets has a police officer stationed every 100 blocks and there is a robber is somewhere in the city.
Can you devise a strategy that guarantees the robber will be spotted by a police officer at some point, no matter how he tries to avoid them?
Note: The officers can see infinitely far, but their running speeds are lower than the speed of the robber.
SOLUTION
Rewarded and Fired
A very rich man has many servants in his mansion. One day as he is about to travel, his night watchman warns him not to board his flight. “I had a dream last night that the plane crashed,” the watchman tells him. The rich man is annoyed at first, but since he is also superstitious himself, he decides not to take the flight.
Later that day as he is watching the news, he sees that his plane did, in fact, crash. He goes over to thank and reward his servant, and then fires him. Why?
SOLUTION
