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# Questions tagged [mathematics]

A puzzle strongly related to mathematical facts and objects, or whose solution needs serious mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.

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### The lake monster

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can't swim. He can run (along the perimeter)...
2k views

### Order order everywhere

Something strange happened yesterday night. It is about a chain of images that I saw while sleeping, in dreams. The following are the sequences I saw: At 1 am, ...
868 views

### Professor Halfbrain and the powers of 2016

Yesterday I met professor Halfbrain at the coffee house. The professor told me that he had been spending his time with computing powers of $2016$ and combining them with powers of $32$. The professor ...
1k views

### The mysterious card in the middle

The referee tells Lefty, Righty, and Middly: "I have picked three positive integers $L,M,R$ with $L<M<R$ and $L+M+R=13$, and I have written these numbers onto the three cards lying face down on ...
2k views

11k views

### Building a 2 mile runway on a 1x1 mile island [closed]

You have a 1-mile long x 1-mile wide island. When taking off from a flat runway, a plane requires a runway of minimum length 2 ...
5k views

### Divide an integer by 2 by replacing 9 with 0

What are examples of integers that halve their values when all 9's in their decimal representations are replaced with 0's?
5k views

### You surely don't want to score 100/100

The Story: Today, the Maths quizzes are handed out by the teacher. You got 100/100. Everyone got 100/100. But you're not happy with it. Everyone's not happy with it. You want to ...
1k views

### One-one communication

5 people are standing in a circle - person A needs to tell his salary to person B, but none of the others should know A's salary. How is this possible, if every person only whispers to the person on ...
4k views

### How Can I Safely Double The Length of A Ladder?

I'm posting this from the roof of a building because I can't figure out a safe way down. I've scoured the roof for anything useful, and all I found was a coping saw. I also found a 100 foot ladder, ...
3k views

### Math with dinosaurs

Doctor Brun was at it for years, but he'd finally got his time machine up and running. His first trip was to a time way back in the past when dinosaurs roamed the Earth. To his surprise, the dinosaurs ...
2k views

### Blackboard cleaning

The blackboard contains 30 integer numbers from 1..2000. Each minute you are allowed to elect some positive integer number x and subtract x from some (chosen by you) of the numbers on the blackboard ...
3k views

### Guess five binary digits!

Person A thinks of a 5 digit binary number. Person B tries to guess the number. B can guess a 5 digit binary number and A will respond with the number of correct digits (digits in the right place). ...
1k views

### Measuring Water with a Holey Cube

You have been given a transparent glass cube, which has a small hole at the center of one of the faces. How can you fill the cube with water occupying exactly one third of its volume? Edit: The ...
A rectangle is tiled by nine squares with side lengths $2,5,7,9,16,25,28,33$ and $36$ (without overlapping and without gaps). What are the side lengths of the rectangle? What does the tiling look ...