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.

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31
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1answer
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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 ...
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1answer
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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 ...
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1answer
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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 ...
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3answers
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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 ...
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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 ...
31
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1answer
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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 ...
31
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3answers
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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 ...
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6answers
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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 ...
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7answers
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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An unusual and very hard number sequence problem

I heard this number sequence problem about 25 years ago from a maths lecturer. What number should go in the place of the question mark in this mathematical sequence: $..., 30, ?, 60, 90, 140, 225, ...
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Are all balls the same weight?

There are 10 balls which come in two possible weights. Using a balance scale at most 3 times, determine whether all the balls are the same weight or not. Notes: I got this riddle from this ...
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Using only 1s, make 29 with the minimum number of digits

Use the minimum number of ones to make 29. Here is the list of operations permitted: "Standard" operations, such as: $x+y$, $x-y$, $x\times y$, $x\div y$ Negation: $-x$ Exponentiation of two numbers:...
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10 9 8 7 6 5 4 3 2 1 = 2016

Add the four basic operators $\times\div+\,\;-$ and optionally brackets to: $10 \quad 9 \quad 8 \quad 7 \quad 6 \quad 5 \quad 4 \quad 3 \quad 2 \quad 1$ To get the total $2016$. Rules: We are ...
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7answers
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Almost impossible Sudoku like puzzle

I was set a puzzle in my math class. I tried to do it using an equation but it didn't work it looked like a trial and error puzzle so I took it into school and the math teachers couldn't solve it. Is ...
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A lonely pawn on the chessboard

Alice and Bob and the referee Conny play the following game with a pawn on a standard $8\times8$ chessboard: In the beginning, Conny places the pawn into the center of a randomly chosen square. All $...
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1answer
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Just do it rebus

$\Large n = \Large a^{-1}\cdot e^{\frac{\huge it}{\huge s}}$ It is a catchy phrase.
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4answers
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Short but impossible math problem

Given these four equations/inequalities: 1x=2 2x=4 3x=3 4x>8 What is x?
28
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5answers
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 ...
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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: ...
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5answers
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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, "...
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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 ...
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1answer
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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 ...
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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 ...
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1answer
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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 ...
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3answers
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Numbers on the blackboard: From 2-2015 to 1-2014

The numbers $ 2, \ldots, 2015 $ are written on a blackboard. Each minute any two numbers $ x $ and $ y $ are wiped out and are replaced by two numbers $\displaystyle \frac { 4x + 3y } { 5 } $ and $...
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Unsolved Mysteries: Magic Square of Squares

This is the first in what will hopefully be a series of Unsolved Mysteries posts. Note that this puzzle has no known solution, nor any proof that a solution is impossible. We will see how ...
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9answers
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A clock for 2017

Design a clock where each number from 1 to 12 is obtained as an arithmetical operation using each digit of 2017 exactly once: for example, 4 could be made as $2\times 7-10$.
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19answers
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Ant walking on a number line

An ant walks on a number line, starting at location $x=7$. Each second, it randomly moves one space either left ($-1$) or right ($+1$), with equal chance. At $x=0$ and $x=10$ are drops of honey; the ...
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7answers
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What's the perimeter of the hexagon?

Consider a hexagon which is equiangular but not equilateral: all angles equal to 120 degrees but four consecutive sides of length $a,b,c,d$ not necessarily equal. What is the perimeter of the hexagon? ...
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Winnie-the-Pooh and the 27 honey pots

Winnie-the-Pooh keeps his $27$ honey pots in the larder. Each pot contains up to $1$ kilogram of honey, and different pots contain different quantities of honey. All $27$ pots together contain $17$ ...
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1answer
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Use three 10's to create 950

Here is an interesting puzzle that I found: You have three 10's. It looks like this: | 0 | 0 | 0 Add one stroke to the diagram to create 950.
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What, the answer isn't the No of the Yes is?

Doorknob knows exactly how to solve this, so I ask him to not answer this question. Well, here's the puzzle: No, an answer is the cube without A, No? The Yes is No. The squared answer, Yes, is to an ...
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10answers
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One prize, infinitely many choices

Having reached the final stage of a game show, you face an endless row of doors labelled $1$, $2$, $3$, ... The game show host has selected a whole dollar amount, and has put this exact amount as a ...
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How do I convince my grandmother?

How do I convince my grandmother (who really hates mathematics) that there exist three positive integers $x,y,z$ that satisfy the equation $28x+30y+31z=3650$?
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One hundred tiles

One hundred tiles are arranged in a $10 \times 10$ square. Each tile is black on one side and white on the other side. Two types of move are allowed: Flip over all four tiles in any $2 \times 2$ ...
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2answers
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Mathematical Rebus II

Mathematical Rebus I Mathematical Rebus III $$\det\frac{\partial(x,y)}{\partial(r,\varphi)}\\ \sum_{n=2}^\infty \ddot{\frac{t^n}{n!}} $$
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Unknown weight of four identical objects

Four identical looking objects weigh 3oz, 5oz, 8oz and 11oz. You do not know which objects weigh what and they are too close in weight to tell by holding them. Using a balance scale, how can you ...
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4answers
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What is the most triangles you can make from a capital “H” and 3 straight lines?

So start with an upper case H, and then draw $3$ straight lines. What is the greatest number of closed triangles that you can form? For example: Note that triangles inside of triangles only count ...
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6answers
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Stargate escape

What a nightmare! When you awake in cold sweat you only remember dazzling colours, flash-lights, dark shadows with far too many arms and the sickening sensation of being dropped from a high place. You ...
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4answers
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Ernie and the Pirates of the Caribbean

A few weeks ago, I dropped in to see Ernie to ask if he was willing to look after the cat while I was on holiday in the Caribbean. “No problem.” he replied then showed me an old leather-covered book, ...
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Make 2 dice out of 3 dice

This question was first posted by standupmaths on youtube: https://www.youtube.com/watch?v=xHh0ui5mi_E He already got some answers but I think this community can probably find a better answer. ...
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4answers
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Lions and Zebras on a Chess Board

The black knight is our lion chasing 8 white bishop zebras which can't capture. Can the zebras evade the lion forever, if team zebra positions all the pieces and has the first turn? Rules: The game ...
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3answers
844 views

Ever increasing highway numbers

A province has 10 cities (arranged in a circular manner). Every pair of cities is directly connected by a straight highway, and each has its own unique number: Highway 1, Highway 2, Highway 3, ..., ...
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4answers
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Arrows on a Chessboard

I've taken an $n$ by $n$ chessboard and drawn an arrow on each square, pointing in one of the eight compass directions. I've done this in such a way that arrows in (orthogonally) adjacent squares ...
26
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1answer
350 views

George Orwell Sudoku

Here is a puzzle I created today. The title is "George Orwell Sudoku" Normal Sudoku rules apply. In every coloured group of three cells the middle digit must equal the sum of the other two ...
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1answer
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The tough one from “A Brilliant Young Mind” (2014)

Great movie by the way. I'm quoting from memory, so I may get the wording wrong. The positive integers are each colored Red, Yellow or Green. Prove that for any such coloring, there must exist ...

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