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Results tagged with mathematics
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user 16990
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.
16
votes
Accepted
How many paths are there?
Assuming that each "movement" moves me exactly one grid square, there are
Because
Alternative way of solving (that arrives at the same solution).
Since this puzzle is tagged "Visual" and not "Math," …
- 3,040
13
votes
Accepted
Alice splits the bill not too generously with Bob
Alice must choose a number with no less than
The lowest such number is
Bob's strategy is:
If we do this, then the score Bob can earn is defined by the following recurrence relation:
We can evaluat …
- 3,040
10
votes
4
answers
409
views
Irregularly Deposited Compound Interest
Suppose you have a very peculiar bank account that obeys the following rules:
The account pays 10% interest per year, generated continuously.
Interest from the account does not compound automatically …
- 3,040
8
votes
2
answers
474
views
Is the Ted-Ed Leprechaun's Magic Bag Unique?
Inspiration:
Ted Ed: This one weird trick will get you infinite gold - Dan Finkel
Codegolf Stack Exchange: Shift Right by Half a Trit - AlephSquirrel
Consider a Magic Bag which has the following pro …
- 3,040
6
votes
Accepted
6
votes
Finding the larger number with a minimal number of questions
Partial answer
The best I can manage is
This is better than we'd be able to get by binary searching for each person's number individually, but still well short of the 1012 the problem asks for.
As a …
- 3,040
4
votes
Making perpetual motion machine from candy-sharing cats
Partial answer to get things rolling.
It is impossible to make a PMM with exactly
Explanation
Start with the following observations.
Observation 1:
Observation 2:
Observation 3:
With those out of …
- 3,040
3
votes
A tournament, and a tight personal schedule
I arrived at the same solution as Desouvi, but I reasoned it from the other direction.
The final answer is
To start with, I observe
This splits the problem into two smaller problems.
But since I al …
- 3,040
3
votes
1000 Batches, 1 Poisoned, 4 Mice, Minimized Costs
Simplified Problem
I'm going to start with a slightly modified version of question 3, and then use the answer to that problem to answer the original questions.
The first problem to solve is:
You visi …
- 3,040
2
votes
3
answers
242
views
Detecting Connected Components on an Infinite Graph after Modification
This puzzle was inspired by thinking about how to implement a system like Factorio's power grid.
Start with an infinite connected undirected acyclic graph.
Graph = A set of nodes (called "vertices") …
- 3,040
2
votes
Are perfect cubes possible?
Partial answer: By Fermat's Last Conjecture, there are no positive integers x, y, z, such that x^3 + y^3 = z^3
Let a+b = x, and c+d = y, and it follows that a+b+c+d cannot be a perfect cube.
- 3,040
1
vote
1
vote
Labyrinth of Teleporters
A deterministic algorithm for exploration.
Other answerers have already created solutions for what to do if you have an algorithm that will return you back to the start (and "move randomly" theoretica …
- 3,040
1
vote
Irregularly Deposited Compound Interest
My own solution
The following is the solution I had when I posted this puzzle. It loses to Albert.Lang's answer, but beats others.
First observation:
Second observation:
Third observation:
That giv …
- 3,040
0
votes
2 Monkeys on a computer
Similar to Marco Salerno's answer, I wrote a computer program to solve the monkey problem.
static void Coconuts(int iterations)
{
Tuple<double, double>[] outcomes = new Tuple<double, double>[iter …
- 3,040