All Questions
Tagged with combinatorics puzzle
566
questions
4
votes
0
answers
144
views
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
1
vote
0
answers
79
views
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
views
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
views
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 ...
- 626
39
votes
1
answer
3k
views
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
views
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
views
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
0
votes
0
answers
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 ...
- 43
0
votes
0
answers
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
views
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 ...
- 99
3
votes
2
answers
427
views
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
views
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 ...
- 183
1
vote
1
answer
210
views
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 (...
- 13
6
votes
1
answer
438
views
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. ...
- 1,837
6
votes
1
answer
335
views
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