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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The Emperor’s Magic Trick: The Omnipotent Compass
This is a follow up question to my previous question: The Emperor’s Command: All Roads Lead to Rome, because our emperor wants more!
The Emperor was pleased that all roads led to Rome, but his thirst ...
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A Logic Puzzle Where No Variable Can Be Determined Without All Six Clues
Six variables 𝐴, 𝐵, 𝐶, 𝐷, 𝐸, 𝐹 are distinct integers from 1 to 10 (inclusive).
They satisfy the following conditions (I've added mathematical definitions on the right to avoid ambiguity):
𝐵 is ...
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The Emperor’s Command: All Roads Lead to Rome
This is follow-up question to All (red and blue) roads lead to Rome
Eight cities lie in a kingdom, with Rome at the center of power.
Every morning, the Emperor shouts a sequence of colors from his ...
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All (red and blue) roads lead to Rome
(This problem is from the 2024 Konhauser Problemfest, written by Stan Wagon.)
Eleven cities, one of them being Rome, are arranged in a circle, with adjacent cities joined by a pair of one-way roads, ...
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4x4 grid with all 7 adjacent colour pairs
Can you paint the cells of a 4x4 grid with 7 colours such that every pair of different colours is orthogonally adjacent at least once?
Bonus: Can you achieve this with one cell unpainted?
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Lights-out variant on a tetrahedron
You have a tetrahedron whose faces are covered in 4 × 4 triangular grids. Each triangular cell has a light and a switch that toggles that light and the three edge-adjacent lights. The blue dots ...
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Two hunters and 1 rabbit in bushes in a circle
We have two hunters and 10 bushes (In a circle). There is also a single bunny, which moves to an adjacent location each turn.
In how many tries will the hunters successfully kill the bunny?
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The Calabash Calculator
You are introduced to the Calabash Calculator, which supports the following operations:
The four basic arithmetic operations, + - × ÷
The six comparison operators, ...
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If we roll a fair dice 36 times then what is the probability that we roll each number (1, 2, 3, 4, 5 and 6) exactly 6 times? [closed]
If we roll a fair dice 36 times then what is the probability that we roll each number (1, 2, 3, 4, 5 and 6) exactly 6 times?
It is an Oxford University interview problem.
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Lights-out variant on an octahedron
You have an octahedron that’s covered in a 2 × 2 triangular grid, i.e., each face is divided into four congruent equilateral triangles (cells). Each cell of the grid hosts a light and a switch that ...
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Separated but Together
Two astronauts are stranded on separate asteroids, more than a million kilometers apart. Each asteroid is a different shape: jagged, irregular, nothing alike.
Desperate for connection, they wonder: is ...
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The Plot Armor of the Galactic Engineer
The puzzle reads:
Suppose you are a galactic engineer. You are building a communication network between many distinct star systems. To prevent signal interference, every single pair of stars must be ...
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Silhouette of a slime mold attempting to mimic a centipede
The following image depicts the little-known* Western Centipede-Mimicking Slime Mold, here seen attempting (with limited success) to take on the form and coloration of a common garden centipede:
But ...
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Lights-out variant on a beveled cube
You have a beveled cube where each face is a 3 × 3 grid of square cells, each edge a 1 × 3 grid, and each corner is a triangular cell. The cells (both square and triangular) have lights on them, of ...
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What is wrong with the proof? [duplicate]
What is wrong with this proof?
Let $x\in\mathbb R$. Then
\begin{align*}
&&x^2+x+1 &= 0&&\\
\implies&&&&\text{(multiply both sides by $(x-1)$)}\\
&&(...
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