All Questions
Tagged with combinatorics puzzle
566
questions
48
votes
2
answers
2k
views
Guessing a subset of $\{1,...,N\}$
I pick a random subset $S$ of $\{1,\ldots,N\}$, and you have to guess what it is. After each guess $G$, I tell you the number of elements in $G \cap S$. How many guesses do you need?
- 3,373
12
votes
2
answers
3k
views
How many ways can we let people into a movie theater if they only have half-dollars and dollars?
My interest in combinatorics was recently sparked when I read about the many things that the Catalan numbers count, as found by Richard Stanley. I picked up a copy of Brualdi's Combinatorics, and ...
- 22.4k
3
votes
2
answers
858
views
13 integers with each set of 12 integers
Take 13 integers. Prove that if any 12 of them can be partitioned into two sets of six each with equal sums, then all the integers are the same.
Does anyone know if the general case with 2n+1 ...
- 5,910
7
votes
1
answer
999
views
Guessing a hidden number on a cube
You are and your friend are given a list of N distinct integers and are told this:
Six distinct integers from the list are selected at random and placed one at each side of a cube. The cube is placed ...
- 8,759
4
votes
1
answer
4k
views
Calculating Total Amount of Money Based on Weight
Dealing with US Dollars...
Assuming we know the weights of half-dollars, quarters, dimes, nickels, and pennies.
Also assuming the weights remain constant (don't change from one quarter to another ...
- 2,123
17
votes
3
answers
3k
views
Cutting a unit square into smaller squares
My algebra professor gave me this puzzle a while back. I'm pretty sure I've found the right solution; nonetheless, I wanted to share it and see if you come up with anything really nice or unexpected.
...
- 4,154
5
votes
1
answer
719
views
There is a 5 by 5 matrix of points on a plane. How many triangles can be formed using points on this matrix?
There is a 5 by 5 matrix of points on a plane. How many triangles can be formed using points on this matrix?
- 51
2
votes
1
answer
333
views
When does an orthomorphism of the cyclic group exist?
I thought I would post (as a puzzle) one of my favourite results in combinatorics. I actually use variants of this result in research quite often. It's not impossible that someone will post an ...
- 21.1k
199
votes
22
answers
124k
views
Taking Seats on a Plane
This is a neat little problem that I was discussing today with my lab group out at lunch. Not particularly difficult but interesting implications nonetheless
Imagine there are a 100 people in line to ...
- 4,949
4
votes
6
answers
5k
views
Finding the Heavy Coin by weighing twice
Suppose you have $100$ coins. $96$ of them are heavy and $4$ of them are light. Nothing is known regarding the proportion of their weights. You want to find at least one genuine (heavy) coin. You are ...
anonymous
96
votes
5
answers
7k
views
Cutting sticks puzzle
This was asked on sci.math ages ago, and never got a satisfactory answer.
Given a number of sticks of integral length $ \ge n$ whose lengths
add to $n(n+1)/2$. Can these always be broken (by ...
- 5,646