All Questions
Tagged with combinatorics puzzle
566
questions
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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....
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1
answer
70
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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
votes
0
answers
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
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
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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
votes
1
answer
84
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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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52
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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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34
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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
votes
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
vote
2
answers
145
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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 ...
- 53
4
votes
1
answer
146
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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
92
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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
views
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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4
votes
0
answers
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
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0
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79
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Solving formulas for Coupon Collector's problem variant
I considered a modified version of the Coupon Collector's problem where there are $m$ transparent balls, $k$ different colors and $c$ balls of each color for a total of $n=ck+m$ balls in the urn.
I ...
- 31
3
votes
1
answer
187
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How to prove whether this grid puzzle is unsolvable/solvable?
[Disclaimer: I have researched a bit before this post and I have found no other questions that address my problem specifically, hence this post]
So I have been made a puzzle concept in a python ...
- 33
0
votes
1
answer
107
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Light and bulb problem from an old maths contest
In a room there is a series of bulbs on a wall and corresponding switches on the opposite wall. If you put on the $n$ -th switch the $n$ -th bulb will light up. There is a group of men who are ...
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39
votes
1
answer
3k
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Is it possible to assemble copies of this shape into a cube?
A couple of friends of mine were discussing a problem concerning this shape:
Is it possible to assemble enough of these to form a cube?
I have discovered a lot of impossible positions but was not ...
- 507
2
votes
1
answer
3k
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Compute the number of ways to reach a point without overshooting puzzle
I am trying to solve the following puzzle:
An ant is trying to get from the origin (0, 0) to X = (13, 4) without overshooting, but he can only move up or right. He always alternates his step sizes ...
- 1,027
2
votes
1
answer
277
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How many ways can I pick a size $3$ set from $\{1, 2, 3, 4, 5, 6, 7, 7, 7\}$ such that at least one is odd?
I am trying to solve the following puzzle:
I have nine cards, where six of them are labelled $1$ through $6$ and the remaining three are indistinguishable and labelled with 7. Calculate the number ...
- 1,027
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0
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56
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k-cycles and permutation of remaining elements in the 100 prisoner problem formula
The original problem can be found here, 100 prisoners problem , where $n=100$ and $n/2 \lt k \le n$. Letting $L(n,k)$ equal the number of permutation on $n$ distinct objects with greatest cycle length ...
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42
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How many locks and keys: combinatorics problem [duplicate]
A village keep all their most precious belongings in a vault. The vault has a certain number of locks, each lock with an individual and specific key. The people in the village want to make sure that ...
3
votes
0
answers
70
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Puzzle of an ant rearranging stacks of seeds in a line [duplicate]
Interesting puzzle that I haven't been able to solve or find a solution to.
An ant rearranges a line of stacks of seeds as follows:
With each iteration, the ant goes to each stack in order and grabs ...
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3
votes
2
answers
427
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Infected Dinner Brainteaser
I came across this brainteaser online that I found quite confusing:
There are $1000$ people having dinner at a grand hall. One of them is known to be sick, while the other $999$ are healthy. Each ...
- 31
3
votes
0
answers
92
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Maximum tiling by Y Hexomino
"Y Hexomino" has a shape as shown in the picture.
What is the maximum number of Y Hexomino that can be placed on a $13\times 13$ chessboard, where each Hexomino does not overlap?
From the ...
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1
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1
answer
210
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The toys problem: Probability of getting two matching good item and a different third Item
I've encountered an intriguing probability problem. I just registered to ask this, so this will be my first post.
Disclaimer: I met this problem in a real setting that's it too convoluted to explain (...
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6
votes
1
answer
438
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Placing the $21$ two-digit primes into a grid, such that primes in adjacent squares have either the same tens digit or ones digit
This is USAMTS round 3, problem 1 of the 2020-2021 Academic Year.
Place the 21 2-digit prime numbers in the white squares of the grid on the right so that each two-digit prime is used exactly once. ...
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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. ...
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