All Questions
29
questions
4
votes
1
answer
146
views
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
0
votes
0
answers
56
views
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
1
vote
2
answers
633
views
What is the optimal strategy for the "100 prisoners problem" when waiting prisoners are told how many drawers the currently active prisoner has opened
Introduction: A description of the original problem can be found on Wikipedia. The best strategy is: each prisoner opens the drawer with their number first and then each subsequent drawer is ...
- 211
1
vote
0
answers
287
views
Rephrase a simple mathy logic problem (yielding solution of an ordered procedure), and its generalized counterpart, into a solvable algorithm.
I'm given a selection of logic puzzles about different entities crossing a river safely (either from the same side to the same other side, or switching sides; utilizing the same boat, with certain ...
- 29
4
votes
1
answer
80
views
How many different "Dwayne" "The Rock" "Johnson" orderings can be made for $n$ Dwayne The Rock Johnsons?
Let me explain. Whenever I hear Dwayne Johnson's name, I immediately start mixing it up in weird ways by saying his name and nickname multiple times but in random orders. For example "Dwayne"...
- 65
1
vote
1
answer
239
views
Winning strategy for the 100 prisoner problem
Is there a 100% guarantee winning strategy to the "100 prisoner problem discussed" here, here, and here?
Basically there's a room with a light bulb and a switch, and 100 prisoners are called one at a ...
- 309
0
votes
1
answer
100
views
How to find the inverse of the method to find the nth lexicographic logical permutation
I'm looking for a proper method to find the nth logical permutation of a particular sequence that is able to return the desired permutation. For example, for a sequence 1234567890, the 100,001st ...
0
votes
1
answer
86
views
Smallest number of turns needed to flip $P$ pencils, $N$ per turn, until they all point opposite their starting direction
Imagine you have P pencils all faced away from you and you can flip them N at a time. Anytime a pencil is flipped its direction changes 180 degrees. Every time you have flipped N pencils that is ...
- 85
0
votes
1
answer
56
views
How to solve this Yes/No query problem where we need to find the number of sets satisfying the given condition?
So let's say we have 2 people playing a game. Let the first person be $A$ and the second person be $B$. So $A$ guesses a number between $1$ and $n$ ( say $x$) and $B$ gives queries to $A$ in form of $(...
- 482
2
votes
2
answers
899
views
Lower Bound on God's Number in the Rubik's Cube
I'm trying to write a project about the Rubik's Cube, and althought it's easy to find out the lower bound (using half turns) is 18, finding a precise proof hereof seems impossible.
How does one proof ...
- 43
1
vote
2
answers
66
views
In how many different ways can tests A, B, C be performed based on the following conditions?
Suppose a patient has to undergo, on the advice and prescription of an expert physician, three
medical tests A, B and C (say a urine test, a blood test, and an X-ray, to be specific). The physician ...
- 2,132
1
vote
1
answer
222
views
fun fact about permutations and identity.
i have been asked to solve the quastion , when i tried and i found it better to prove first the lemma (both the lemma and the quastion need to be proven):
let $\sigma \in S_n$ be a permutation from {...
- 987
1
vote
2
answers
5k
views
The permutation/combination puzzle: What are the maximum number of tickets possible in a game of Tambola?
Tambola is an interesting game which is played by numbers(between 1-90) being called out and players crossing out the numbers on the ticket. Prizes are won on particular patterns.
Facts about the ...
- 11
30
votes
2
answers
2k
views
Bruteforcing a keypad lock
A particular lock at my university has a keypad with the digits 1-5 on it. When pressed in the correct permutation of those five digits, the lock will open.
Obviously, since there are only 120 ...
- 437
3
votes
1
answer
92
views
Placing zeroes puzzle
In this puzzle, you have to place enough zeroes to make a number have a certain number of digits. For example you are expected to take the 3-digit number $123$ and are expected to make it 5 digits. So ...
- 195