All Questions
Tagged with combinatorics puzzle
81
questions with no upvoted or accepted answers
17
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0
answers
515
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History of a combinatoric problem: exchanging numbers by throwing stones
Another user recently asked a question on the Puzzling stack: Two spies throwing stones into a river. Suitably generalised, it becomes:
Two spies (Alice and Bob) need to exchange a message. Each ...
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714
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Optimal strategy for guessing a binary string
I would have thought this was well known, but I have not been able to track down a reference.
Suppose you are trying to guess an $n-$digit binary string. At any point you may guess all or any portion ...
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8
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431
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Light bulbs in a high dimensional grid
Consider a $n \times n \times n$ array of light bulbs. In each step, one can flip lights from on to off and off to on along a 1d row in the $x$-, $y$- or $z$-axis.
Suppose one has a configuration that ...
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Finding coefficient $a_{1996}$ if $\;\prod_{n=1}^{1996}(1+nx^{3^n})=\sum_{n=0}^m a_nx^{k_n}$
This is from a math contest. I have solved it, but I'm posting it on here because I think that it would be a good challange problem for precalculus courses. Also, it's kind of fun.
Write the ...
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6
votes
1
answer
335
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Minimum swaps to put an array into desired order, where some elements are identical/repeated
Inspired by a word game Waffle, see footnotes if interested. The abstracted problem:
You're given an input array of letters, some of which might be identical (i.e. repeated), e.g. ...
- 15.5k
6
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134
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Knights and knaves on a square grid
Today Gathering For Gardner posted a video by Yoshiyuki Kotani called "Liar/Truth Teller Patterns on Square Planes".
The idea is that you fill a grid with knights and knaves so that both the knights ...
- 5,072
6
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0
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643
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A puzzle with some jumping frogs
(The following puzzle is ispired by this nice video of Gordon Hamilton on Numberphile)
In a pond there are $n$ leaves placed in a circle, for convenience they are numbered clockwise by $0,1,\ldots,n-...
user126526
5
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Deceptively difficult coin weighing puzzles
A coin weighing problem is a problem that looks something like this:
You have twelve coins. Eleven of them weigh the same; one of them is either heavier or lighter than the other eleven. You want ...
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4
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98
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Which abelian groups and odd integers lead to a well-posed weights puzzle?
Consider the following puzzle (which I quote from here):
In a collection of 101 balls, each ball weighs a whole number of pounds. If any one is removed from the collection, the remaining balls can be ...
- 2,243
4
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144
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No two adjacent bulbs on
The problem is to count number of configuration of $9$ bulbs on a $3\times 3$ grid, where no two bulbs that are adjacent are switched on.
I solved this problem in a very ad-hoc kind of manner, the ...
- 378
4
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109
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What percent of lighted grids are walkable: a trick-or-treating problem
I am a math teacher that likes to invent fun math problems to explore. Here is one I have been investigating for a little while and have made little progress on because the number of possible $n \...
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4
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1
answer
108
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Chinese Checkers Puzzle: Pawns Movement
I have a question how to solve the following problem.
First, we have a chess board and two pawns located at $a1$ and $a2$. Our goal is to move them to the location $h7$ and $h8$. The rules for a pawn ...
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4
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159
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Minimizing floor space needed to store $N$ unit cubes, subject to two placement rules
There is a store room which has only three sides all touching each other perpendicularly, the sides can be defined as: two infinitely large walls and one infinitely large floor.
There are $N$ cubes ...
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4
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Smallest number not expressible using first $n$ powers of $2$ (exactly once each), with $+$, $-$, $\times$, $\div$, and parentheses?
Motivation
Solution to this problem is a lower bound for a more general problem.
Problem
Given first $n$ powers of two: $1,2,4,8,16,\dots,2^{n-1}$ that all need to be used exactly once per number ...
- 12.5k
4
votes
1
answer
229
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spaghetti hoops combinatorics variation
You may have heard about the classic spaghetti hoops combinatorics problem, which has been stated like this:
"You have N pieces of rope in a bucket. You reach in and grab one end-piece, then reach in ...
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