All Questions
Tagged with combinatorics puzzle
566
questions
228
votes
4
answers
11k
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How many fours are needed to represent numbers up to $N$?
The goal of the four fours puzzle is to represent each natural number using four copies of the digit $4$ and common mathematical symbols.
For example, $165=\left(\sqrt{4} + \sqrt{\sqrt{{\sqrt{4^{4!}}}...
- 5,861
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
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
87
votes
10
answers
13k
views
100 Soldiers riddle
One of my friends found this riddle.
There are 100 soldiers. 85 lose a left leg, 80 lose a right leg, 75
lose a left arm, 70 lose a right arm. What is the minimum number of
soldiers losing all 4 ...
59
votes
2
answers
2k
views
An illusionist and their assistant are about to perform the following magic trick
Let $k$ be a positive integer. A spectator is given $n=k!+k−1$ balls numbered $1,2,\dotsc,n$. Unseen by the illusionist, the spectator arranges the balls into a sequence as they see fit. The assistant ...
- 90.7k
50
votes
7
answers
49k
views
In a village, $90\%$ of people drink Tea, $80\%$ Coffee, $70\%$ Whiskey, $60\%$ Gin. Nobody drinks all four. What percentage of people drinks alcohol?
In a small village $90\%$ of the people drink Tea, $80\%$ Coffee, $70\%$ Whiskey and $60\%$ Gin. Nobody drinks all four beverages. What percentage of people of this village drinks alcohol?
I got this ...
- 639
50
votes
7
answers
79k
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How many triangles
I saw this question today, it asks how many triangles are in this picture.
I don't know how to solve this (without counting directly), though I guess it has something to do with some recurrence.
How ...
- 23.2k
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
47
votes
7
answers
6k
views
How many scientists can survive?
Yesterday the aliens took 100 scientists from Earth as prisoners. They want to test how smart the humans are.
The aliens made 101 headbands, numbered from 1 to 101. On the contest day, they throw ...
- 1,151
43
votes
3
answers
3k
views
Why the "self-referential number" function eventually fixes every point
Given an 8-digit decimal number $N$, output a new 8-digit number $f(N)$ whose first digit is the number of zeroes in $N$, the second the number of ones, ..., the seventh the number of sixes, and the ...
- 19.7k
43
votes
2
answers
3k
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Proving a jigsaw is possible
This is an offshoot of this question.
Suppose we have jigsaw puzzle pieces which are basically squares but where each side can be either straight, concave or convex. An example of three such pieces ...
- 5,716
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
37
votes
3
answers
2k
views
Guaranteed Checkmate with Rooks in High-Dimensional Chess
Given an infinite (in all directions), $n$-dimensional chess board $\mathbb Z^n$, and a black king. What is the minimum number of white rooks necessary that can guarantee a checkmate in a finite ...
- 8,759
31
votes
5
answers
38k
views
Puzzle of gold coins in the bag
At the end of Probability class, our professor gave us the following puzzle:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1....
- 11k
30
votes
6
answers
3k
views
A beautiful game of gold and silver coins
A stack of silver coins is on the table.
For each step we can either remove a silver coin and write the number of gold coins on a piece of paper, or we can add a gold coin and write the number of ...
- 1,829