# Questions tagged [mathematics]

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

3,296 questions
Filter by
Sorted by
Tagged with
3k views

### How to get a bowl with one liter of water

You are given a rectangular bowl with size 5 x 30 x 40 cm and you should put exactly one liter of water into the bowl. You go to your kitchen, where you can put the water directly into the bowl from ...
2k views

### A Cave in the Black Mountains

Across the Deadly River, among the Black Mountains, is a mystical cave. Anyone who enters the cave finds within it a single gold coin, which may be freely taken. Once you leave the cave, you can never ...
2k views

### Computation without a computer

In the number $(1+\sqrt{3})^{2015}$, what is the 224th digit after the decimal point? You may NOT use a calculator, computer, or any electronic aid to answer this question. Only pen(cil), paper, and ...
2k views

### Knights on a Torus

An 8×8 chessboard is in the shape of a torus. (This means that the board "wraps around" - you can go left from a2 and come out on h2, for instance. It also works vertically - you can go up from f8 and ...
3k views

### Ernie and the Alchemist's Gift

For Ernie, the task of choosing Christmas presents for his friends is always a struggle. I think that is because, while he finds it easy to solve problems relating to machines, mathematics, and ...
3k views

### Ernie and the Island of Stability

Unfortunately, it appears that I may have misled you a little in this puzzle (as you probably know - my memory of events isn't always perfect). When I was writing it, I re-checked the Kzijekistanian ...
3k views

### Cross-road optimization - what is the proper way to solve this type of puzzle?

This puzzle has 3 levels of increasing complexity. Each "level" is separate and complete, so feel free to post partial solutions to the individual levels only. I'm most interested in the ...
7k views

### Noughty Mathematics Question

Use your imagination to follow these instructions: Take out an imaginary piece of paper. Turn it 90° clockwise. Make a mental note to use right-justification and nice, tight kerning and leading. In ...
8k views

### Aside from brute force, how can I solve this puzzle?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market. When asked how many she had, she replied: Son, I can't count past 100 but I know that: If you ...
9k views

### How many steps are visible on the Escalator?

Alice walks down an upward escalator and counts 150 steps. Bob walks up the same escalator and counts 75 steps. Alice takes three times as many steps in a given time as Bob. How many steps are ...
5k views

### A mathematical riddle

Three letters can define me, Sometimes even just one. Try to derive the answer, And you'll find just me. I'm so fast, I'm so slow, Up or down I will go. Some are based on different things, Though all ...
5k views

### A robot surviving on top of a 3x3 platform

A robot sits in the central square on top of a 3x3 platform. The robot can move up, down, left or right, but if it steps off the platform it will crash and die. You can preprogram the robot to make a ...
5k views

### Teacher, teacher on the wall, Who's the dumbest of them all?

A maths teacher writes a very large number on the blackboard and asks her pupils (of whom there are $n$ in the room) about its factors. The first pupil says, "The number is divisible by 2." The ...
6k views

2k views

### Just do it rebus

$\Large n = \Large a^{-1}\cdot e^{\frac{\huge it}{\huge s}}$ It is a catchy phrase.
6k views

### Short but impossible math problem

Given these four equations/inequalities: 1x=2 2x=4 3x=3 4x>8 What is x?
791 views

### Dissecting the holey octomino into a square

This is a pure dissection problem, with no added twists. Cut the holey octomino (i.e., a square with the middle third removed) into several pieces, and reassemble those pieces into a square with no ...
7k views

### Make 11 from five identical digits

At a tender age my father introduced me to an arithmetic game: making the number 11 from five single digits using only the basic operators listed here: ...
4k views

### First odd number in a “number dictionary”

All numbers between 1 and 1010 are written out and ordered alphabetically into a dictionary (as the only entries). Spaces and hyphens are removed. 1024 would then be "onethousandtwentyfour". Also, "...
2k views

### Finding digits that sum to 15

Rand and Rubio are playing a game in which they each take turns to pick a digit between 1 and 9, without replacement (i.e. all digits chosen are distinct). If one of them manages to get three digits ...
3k views

### The largest Monday number

A Monday number is a positive integer $N$ with the following three properties: The decimal representation of $N$ does not contain the digit 0 The decimal representation of $N$ does not contain any ...
3k views

### Can you see out of the forest?

You are standing at the centre of a circular forest of radius 500 metres. The trees of this very regularly planted forest stand in a precise rectangular lattice on the plane, each 10 metres from the ...
2k views

### How many silver marbles does Paul have?

Peter, Paul and Mary have between them 282 marbles. Though of the three friends, it is Peter who has the most marbles, he is the one with the fewest silver marbles, just the square root of the ...
1k views