All Questions
32
questions
1
vote
1
answer
177
views
Total number of distinct possible marks for given number of questions and marks (ZIO 2023 Q1)
Q. There is an exam with N problems. For each problem, a participant can either choose
to answer the problem, or skip the problem. If the participant chooses to answer the
problem and gets it correct, ...
- 11
1
vote
0
answers
47
views
Squared multiplicty minimization in multiple set choosing problem
The problem is the IOI 2007 competition's Sails problem. It has also appeared in Pranav A. Sriram Olympiad Combinatorics notes (Chapter 1 Exercise 14). I copied the problem description from Pranav. ...
- 11
1
vote
0
answers
95
views
Building a primitive programming language for solving math olympiad problem(TSTST 2015)
There was a 6th problem on USA TSTST 2015:
A Nim-style game is defined as follows. Two positive integers $k$ and
$n$ are specified, along with a finite set $S$ of $k$-tuples of
integers (not ...
- 51
2
votes
1
answer
139
views
HMMT 2014 #9, how many times has Lucky performed the procedure when there are 20 tails-up coins?
There is a heads up coin on every integer of the number line. Lucky is initially standing on the zero
point of the number line facing in the positive direction. Lucky performs the following procedure: ...
- 2,031
1
vote
1
answer
142
views
Sum of Product of Min, which is related to the Pentagonal number theorem.
The title looks a little bit weird. The problem comes from the Atcoder Beginner Contest 279-Ex: Sum of Prod of Min:
Problem: You are given positive integers $n$ and $m$. Here, it is guaranteed that $n ...
- 1,008
1
vote
1
answer
92
views
Repainting of chessboard with restrictions
Assume an $8\times 8$ chessboard with the usual coloring. You may
repaint all squares (a) of a row or column (b) of a $2\times 2$
square. The goal is to attain one black square. Can you reach the
...
- 17k
2
votes
0
answers
34
views
Astronomer watching planets in a solar system
There is exactly one astronomer on every planet of a certain system. He watches the closest planet. The number of the planets is odd and all of the distances are different. Prove that there one planet ...
- 162
2
votes
0
answers
166
views
Greedy algorithm minimizes the sum
There are $n$ positive numbers (not necessarily distinct). In every step, we
can select two numbers and replace each of it with the sum of the two
numbers. Prove that in any amount of steps, selecting ...
- 1,909
0
votes
1
answer
56
views
Number of ways of traversing a graph through all of its nodes?
A lift has $N$ stops ($1,2,3,4,...,N$), hence have $N(N-1)$ distinct rides of travelling from floor $A$ to floor $B$ such that $A\neq B$. How many arrangements of these rides form a continuous trip ...
- 51
1
vote
1
answer
768
views
Sorting an array using reverse
I ran into an Olympiad question recently, and one challenging question surprised me:
We have an array $A$ with $n$ elements. $\operatorname{Rev}(i, j)$ for $1 \leq i < j \leq n$ reverses subarray $...
15
votes
3
answers
941
views
Partition 100 people, 4 from each country into 4 groups with conditions
This is a problem from the $2005$ All-Russian Olympiad. Problem is as follows:
$100$ people from $25$ countries, four from each country, sit in a circle.
Prove that one may partition them onto $4$ ...
- 381
1
vote
1
answer
87
views
An optimization problem to find the consecutive day subset with maximum value - ZIO $2006$, P$1$
Hello everybody! The above problem is a combinatorics problem I got wrong. :( This is ZIO $2006$, P$1$.
For the first part, I got as answer: $3$ which is wrong. What I did to try my value which I ...
- 779
2
votes
1
answer
105
views
determine the least number of rounds that needs to be played so that every child is satisfied
A group of N children, who are numbered 1, 2, . . . , N, want to play hide and seek. In a single round of hide and seek, there will one seeker, and N −1 hiders. Children like to hide and not seek and ...
- 49
0
votes
2
answers
113
views
ways of expressing T as the sum of four elements of S. [closed]
In this task you will give a sequence of numbers $S$ of length $N$. Every element
will be greater than or equal to 1. We write $S[i]$ to refer to the $i$-th element of the
sequence. For example $S = (...
- 49
0
votes
1
answer
149
views
the number of 1’s in it is at least as much as the number of 0’s
You are given a list of $0$’s and $1$’s: $B[1]$, $B[2]$, . . . , $B[N]$. A sublist of this list is
any contiguous segment of elements—i.e., $A[i]$, $A[i + 1]$, . . . , $A[j]$, for some $i$ and $j$.
A ...
- 49