All Questions
9
questions
1
vote
0
answers
66
views
Minimum rounds to exchange information among n people
Suppose there are $n$ people and all of them have unique information. In one round, two people can interact and tell each other all information they know. In total, how many round may be required so ...
- 1,334
1
vote
0
answers
211
views
Two equivalent ways to measure overrepresentation
Context
Let say $S\in\mathbb{N}$ is the number of votes cast and $N\in\mathbb{N}$ is the number of seats in the parliament. We may assume $N\leq S$. The votes are distributed among $K$ political ...
- 1,001
1
vote
1
answer
72
views
Construction of a vector consisting of entries with a peculiar pattern
Note: A similar problem was asked in this MO post, but no importance was attached to order of nonzero numbers and zeros
Consider constructing a $n$-tuple of numbers $v=(a_1,a_2,\ldots,a_n)$ consisting ...
- 7,085
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
1
vote
2
answers
69
views
Show that it is not possible for $A$ and $B$ to meet at a point
Two friends $A$ and $B$ are initially at points $(0,0)$ and $(12,7)$ respectively on the infinite grid plane. $A$ and $B$ takes steps of sizes $4$ and $6$ units respectively along the grid lines. Show ...
- 2,132
0
votes
1
answer
76
views
Manipulation with strings riddle.
Starting with the "string" $PI$, can I or not transform it into the "string" $PK$ by applying the following rules (each rule can be used any number of times, in any order, and $x$ and $y$ represents a ...
- 1,072
2
votes
1
answer
4k
views
How many $3$ digit even numbers can be formed by using digits $1,2,3,4,5,6,7$, if no digits are repeated?
How many $3$ digit even numbers can be formed by using digits $1,2,3,4,5,6,7$, if no digits are repeated?
ATTEMPT
There are three places to be filled in _ _ _
I wrote it like this
_ _ $2$
_ _ $4$
...
- 3,458
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
9
votes
3
answers
3k
views
Puzzle: A coin rolls without slipping around another coin
If a coin rolls without slipping around another coin of the same or
different size, how many times will it rotate while making one
revolution?
The proof given is like this:
Cut the curve open ...
- 22.5k