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Results tagged with mathematics
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user 87103
A puzzle related to mathematical facts and objects, whose solution needs mathematical arguments. General mathematics questions are off-topic but can be asked on Mathematics Stack Exchange.
13
votes
Which parent should you start playing against?
Mary should play her first game against
To prove this, notice that if $n$ were even,
For the case presented in the puzzle, with $n$ odd:
- 1,059
2
votes
Accepted
At what point will the logicians reach their final answer?
This was inspired by AxiomaticSystem's answer.
Though the axiom of choice is popular among logicians planning to perform a supertask, I won't actually need it here.
The earliest round at which the gam …
- 1,059
5
votes
Accepted
Missing Game Archive 1 - What was the number?
The value of N is
Reasoning:
The guesses with missing digits were:
- 1,059
7
votes
Accepted
Can I divide the candies among the kids so that everyone is happy?
This is
You can use the following strategy:
Why this works:
- 1,059
1
vote
Prisoners and warden game, again?
I can almost prove that a lower bound is
Conditional on this statement which is reasonable, but I have not been able to prove:
If that statement is assumed, we can renumber if necessary so that
It …
- 1,059
6
votes
Accepted
Another “divide the candies” puzzle
Can you always divide the candies so that both kids are happy?
Proof:
- 1,059
5
votes
Fewest number of prisoners needed
I have a solution that uses
The idea is similar to isaacg's solution, but in a different setting.
This works because
- 1,059
10
votes
Accepted
Arithmetic-progression-free Latin squares
Alex's answer gives a set of values of $n$ for which an AP-free Latin square exists, namely
In fact, no other values of $n$ can work:
- 1,059
13
votes
Connect the Dots: The Sharpest Path Wins
These feel like they should be optimal, but I'm not sure how to prove it.
1×n
3×n, n≥3 odd
m×n, both ≥5 odd
m×n, at least one even
- 1,059
5
votes
Accepted
Moving water by repeated equilibration
Pranay's answer
To prove this, we first note that any strategy worth considering is equivalent to a list of pairs of tanks to equilibrate. We will further assume that this list is finite: any infini …
- 1,059