All Questions
8
questions
2
votes
0
answers
75
views
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
views
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
7
votes
3
answers
169
views
Turning on a nuclear briefcase with the smallest possible number of keystrokes
On the front panel of the "nuclear briefcase" there are $12$ buttons. Each button controls its own switch: pressing it toggles it from ON to OFF and back. The initial position of the ...
- 697
5
votes
1
answer
163
views
Minimal number of questions to identify a subset
This is a curiosity question.
Recently I stumbled across the following problem :
Given three integers $k,m, n$ such that $m+k\leq n$. A friend chooses a subset $S\subseteq\lbrace1,\ldots,N\rbrace$...
- 13.8k
5
votes
1
answer
149
views
Optimizing a winning strategy for a quick tabletop game
A friend of mine recently shared the following puzzle with me:
Puzzle: A circular turntable is divided into four congruent quadrants by two perpendicular lines. (Think of a circle in the $xy$-...
- 22.9k
9
votes
1
answer
1k
views
Identify a truth-teller among a group of truth-tellers and (honest) liars.
This question is inspired by this thread. In that thread, a liar may both tells lies and truths. However, in my version, liars always lie.
Main Question. A group of people consists of $m$ truth-...
- 49.8k
13
votes
3
answers
2k
views
An invisible ghost jumping on a regular hexagon
Given a regular hexagon and an invisible ghost at one of the vertices of the hexagon (we don’t know which). We have a special gun, that can kill ghosts. In a step we are able to shoot the gun twice (i....
- 1,516
8
votes
1
answer
330
views
Removing points from a triangular array without losing information
I'm trying to find insights about the following puzzle, to see if I can find it on the OEIS (and add it if it's not already there):
Suppose I give you a triangular array of light bulbs with side ...
- 5,072