All Questions
Tagged with combinatorics puzzle
566
questions
2
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Dividing $N$ coins into at most $K$ groups such that I can get any number of coins by selecting whole groups
Problem
Inspired from Dividing $100$ coins into $7$ groups such that I can choose any number of coins by selecting whole groups . I am interested in the number of possible ways we can get such a split....
- 1,171
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1
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Dividing $100$ coins into $7$ groups such that I can choose any number of coins by selecting whole groups
The problem goes somewhat like this:
Let's say that we have 100 coins. Now, I have to split these 100 coins into seven different groups such that I can choose any number of coins only by selecting ...
user1319345
4
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0
answers
97
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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 ...
- 2,171
1
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0
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40
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Number of paths with $m$ good pairs of moves [duplicate]
Consider the set $S$ of all paths from $(0, 0)$ to $(n, n)$, formed by sequences of $2n$ moves of the form $(a, b) \rightarrow (a, b + 1)$ or $(a, b) \rightarrow (a + 1, b)$, such that at any point $(...
- 378
2
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0
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75
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Smallest number of groups
Eighty-four developers sign up to contribute to a public open-source project. You need to divide the developers into $n$ subteams such that each contributor is on exactly one team. Their personalities ...
- 378
0
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1
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83
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Largest collections of subsets [closed]
I need to find largest collection of subsets of $\{1,\ldots, 84\}$ such that each subset has size 5 and any two distinct subsets have exactly one element in common.
Any help is appreciated, Thanks
- 378
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Cinema Hall Seating Problem [duplicate]
There are n people in line to enter a cinema that own n seats. Each of the n people have an allotted seat in the cinema hall where they are supposed to sit. The first person forgets his/her seat ...
0
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Maximum Line Segments in an n × n Grid Without Loop formation
Exploring Proof for Maximum Line Segments in an (n * n) Grid Without Loop Formation
Hello Math SE community,
I am investigating how to maximize the number of line segments in an $(n * n)$ grid ...
3
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1
answer
82
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You pick $N$ positive integers between $1$ and $M$ without replacement. If you add another number, what is the probability the maximum hasn't changed?
You initially start with all the integers between $1$ and $M$. You then pick $N$ of them randomly, without replacement, to generate a new set of $N$ non-repeating numbers. The maximum of this set is $...
3
votes
1
answer
124
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Given 99 bags of red and blue sweets, is there a selection of 50 bags containing at least half of each type of sweet?
Assume you have 99 bags containing sweets of two kinds, say blue and red.
Is it always possible to pick out 50 bags such that you have at least half the total of red sweets and half the total of blue ...
- 41
1
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2
answers
143
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Simple solution to random walk
The final score of a football match was 4:3 in favour of the home team. How many ways could the result have gone if there was a period of the match when the away team was leading? I have learnt of a ...
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4
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1
answer
141
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Formalising the problem and create a proof for the game "Waffle"
Waffle is an online game at https://wafflegame.net/daily.
It consists in moving letters (swapping them) to recreate the original words. While you have 15 moves, it can be done in 10. I usually try to ...
- 1,125
1
vote
2
answers
91
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$2n$ knights around a table with namecards, is it possible that for every rotation there is exactly one person with a correct namecard?
I need help with the following puzzle:
Consider a round table which hosts $2n$ knights. At each seat, there is a namecard of one knight. The knights don't necessarily sit in front of their own ...
- 184
1
vote
1
answer
92
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A combinatorics and divisibility puzzle [closed]
I've recently encountered the following puzzle that seems a bit too "mathy" for Puzzling Stack Exchange so I decided to ask here. This is not a homework.
The numbers from $1$ to $15$ must be ...
- 2,183
2
votes
2
answers
111
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Smallest number of absent workers in a factory
I am trying to solve a brainteaser and would like some direction if my line of thought is correct...
At a worker plant, 25 workers were absent on Monday, 22 absent on Tuesday and 19 absent on ...
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