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Námsleið
Description:
The semester is coming to an end so it is time to plan your
studies and choose courses for the next semester. Oh no! This
list is so confusing! Each course has so many prerequisites!
With such a chaotic layout, is it even possible to sign up for
and complete all the courses in any... | 29,000 |
Níulegasti grunnurinn
Description:
Jörmunrekur was playing around with writing some numbers in
different bases. He started by trying $203433$. His favourite number is
nine, so he doesn’t particularly care for this number. But if
he writes it in base $16$
it becomes $31AA9$ which
is a clear improvem... | 29,001 |
Núll og tveir
Description:
Arnar and Arnar are looking at numbers together. Arnar only
likes the digit $0$ while
Arnar only likes the digit $2$. Since Arnar and Arnar are
friends, they like numbers that have each others’ favorite
digits. The numbers are however not allowed to contain any
other digi... | 29,002 |
Obfuscation
Description:
It is a well-known fact that if you mix up the letters of a
word, while leaving the first and last letters in their places,
words still remain readable. For example, the sentence “tihs
snetncee mkaes prfecet sesne”, makes perfect sense to most
people. If you remove all spaces f... | 29,003 |
Ocean Currents
Description:
For a boat on a large body of water, strong currents can be
dangerous, but with careful planning, they can be harnessed to
help the boat reach its destination. Your job is to help in
that planning.
At each location, the current flows in some direction. The
captain can choos... | 29,004 |
Ocean Monument
Description:
Steve has stumbled across an ocean monument and would like
to raid it. He has put on his best set of armor and brought his
favorite trident in search of the rumored sponge room.
The monument is protected by a lot of angry guardians and
elder guardians. The mobs are very strong,... | 29,005 |
Ocean's Anti-11
Description:
Note that this is an easier version of the problem
anti11hard.
Danny Ocean likes many things: casinos, elaborate heists,
and complicated romantic relationships. But it’s a little-known
fact that Danny loves binary strings most of all — binary
strings of any length and comp... | 29,006 |
Ocean's Anti-11 (Hard)
Description:
Note that this is a harder version of the problem
anti11.
Danny Ocean likes many things: casinos, elaborate heists,
and complicated romantic relationships. But it’s a little-known
fact that Danny loves binary strings most of all — binary
strings of any length and co... | 29,007 |
Octopus Game!
Description:
It is this time of annual Octopus Game, a survival game
where the winner stands to win millions of dollars, sponsored
by His Excellency, Lord Pooty! Today is Day
$1$ of the Octopus Games
where the first round of culling begins! You are tasked with
organising the games for... | 29,008 |
Odašiljači
Description:
The mayor has decided that it is high time to implement a
new system of television transmitters. The city can be
represented as a segment of the length $D$ on which there are
buildings of different heights. The width of a
building is negligible. On top of some buildings,
tel... | 29,009 |
Odd A's, Even B's
Description:
Fredrik prefers to have his life in perfect order. His i’s
should be dotted, his t’s should be crossed, his a’s should be
odd and his b’s should be even.
Odd a’s? Even b’s? You see, Fredrik is a great fan of the
Swedish pop wonder ABBA. As a tribute, he likes writing songs
... | 29,010 |
Odd Binomial Coefficients
Description:
You might be familiar with the binomial coefficient
${m \choose k}$ defined as
${m \choose k} =
\frac{m!}{k!(m-k)!}$, where $m$ and $k$ are non-negative integers and
$k \leq m$. Let
$T_2(n)$ be the number of
odd binomial coefficients such that $0 \le k \le... | 29,011 |
Odd Echo
Description:
ECHO! Echo! Ech...
You love shouting in caves to hear your words echoed back at
you. Unfortunately, as a hard-working software engineer you are
not lucky enough to get out that often to shout in caves.
Instead, you would like to implement a program that serves as a
replacement fo... | 29,012 |
Odd Gnome
Description:
According to the legend of Wizardry and Witchcraft, gnomes
live in burrows underground, known as gnome holes. There they
dig up and eat the roots of plants, creating little heaps of
earth around gardens, causing considerable damage to them.
Mrs. W, very annoyed by the damage, has to... | 29,013 |
Odd Man Out
Description:
You are hosting a party with $G$ guests and notice that there is an
odd number of guests! When planning the party you deliberately
invited only couples and gave each couple a unique number
$C$ on their invitation.
You would like to single out whoever came alone by asking all
... | 29,014 |
Odd and Even Zeroes
Description:
In mathematics, the factorial of a positive integer number
$n$ is written as
$n!$ and is defined as
follows:
The value of $0!$ is
considered as $1$.
$n!$ grows very rapidly
with the increase of $n$.
Some values of $n!$
are:
You can see that for some va... | 29,015 |
Oddities
Description:
Some numbers are just, well, odd. For example, the number
$3$ is odd, because it is
not a multiple of two. Numbers that are a multiple of two are
not odd, they are even. More precisely, if a number
$n$ can be expressed as
$n = 2 \cdot k$ for some
integer $k$, then
$n$ ... | 29,016 |
Odds of Mia
Description:
Instead, a roll is scored as follows:
* Mia ($12$ or
$21$) is always
highest.
* Next come doubles ($11$, $22$, and so on). Ties are broken
by value, with $66$
being highest.
* All remaining rolls are sorted such that the highest
number comes first, wh... | 29,017 |
Odometer Analysis
Description:
Tommy Catkins wants to buy a used car, and has asked you to
help him figure out if it has been serviced appropriately. You
happen to know with certainty that the only previous owner of
the car Tommy is interested in was a travelling salescat who
drove at least $2\, 000$
... | 29,018 |
Off-World Records
Description:
As humans work toward establishing a permanent presence on
other planets and their moons, as well as on our own moon,
various sporting bodies are under pressure to rethink the
notion of a world record. Traditionally an athlete on
Earth sets a new world record in a particu... | 29,019 |
Office Building
Description:
Company Z has purchased a land lot for their new office
building. The land is shaped like a rectangular grid with
$r$ rows and $c$ columns, in which each cell has a
tree. The age of each tree is known.
Because Company Z is at the innovative front of the world,
their new of... | 29,020 |
Office Number
Description:
Nathan is a mathematician at a famous university who often
sees patterns in the world around him. One day he notices that
his office number, which happens to be $224$, has an interesting property: it
can be written as a sum of non-negative powers of its digits.
In particular,... | 29,021 |
Office Space
Description:
Your company is moving to a new, larger office building. The
new office is a rectangular space that will eventually be
populated with cubicles. Your employees want to request
particular positions for their cubicles, so you are setting up
a system that lets them make these requ... | 29,022 |
Ograda
Description:
Matija needs to paint his old fence. The fence is made from
$N$ planks, each
$1$ cm in width and
varying in height. To do this easy and fast, he bought himself
a Super Paint Roller Deluxe. The paint roller is $X$ cm wide. The Super Paint Roller
Deluxe model comes with a catch, h... | 29,023 |
Oil
Description:
A large part of the world economy depends on oil, which is
why research into new methods for finding and extracting oil is
still active. Profits of oil companies depend in part on how
efficiently they can drill for oil. The International Crude
Petroleum Consortium (ICPC) hopes that ext... | 29,024 |
Oktalni
Description:
Slavko is learning about different numeral systems. Slavko
is not the brightest when it comes to math, so he is starting
out converting binary numerals to octal. The algorithm Slavko
uses is this:
* Pad the binary numeral with zeros on the left until the
number of digits is di... | 29,025 |
Okvir
Description:
Mirko has assembled an excellent crossword puzzle and now he
wants to frame it. Mirko’s crossword puzzle consists of
$M \times N$ letters, and
the frame around it should be $U$ characters wide on top,
$L$ characters on the
left, $R$ characters on
the right and $D$
charact... | 29,026 |
Okviri
Description:
“Peter Pan frames” are a way of decorating text in which
every character is framed by a diamond- shaped frame, with
frames of neigbhouring characters interleaving. A Peter Pan
frame for one letter looks like this (‘X’ is the letter we are framing):
```
..#..
.#.#.
#.X.#
.#.#.
..#..
```... | 29,027 |
Old School Days
Description:
I don’t know how you feel about your school time, but I
become maudlin when I remember those days. One of our teachers
told us at the final year that among all the educational
institutions in life one misses his/her school days the most.
And yes, I miss those days a lot.
L... | 29,028 |
Old Wine Into New Bottles
Description:
Wine bottles are never completely filled: a small amount of
air must be left in the neck to allow for thermal expansion and
contraction. If too little air is left in the bottle, the wine
may expand and expel the cork; if too much air is left in the
bottle, the win... | 29,029 |
Older Brother
Description:
Your older brother is an amateur mathematician with lots of
experience. However, his memory is very bad. He recently got
interested in linear algebra over finite fields, but he does
not remember exactly which finite fields exist. For you, this
is an easy question: a finite fi... | 29,030 |
Olympiad Training
Description:
Besides the prestigious ACM-ICPC contest, Nha Trang
University also hosted the Vietnamese Collegiate Olympiads in
Informatics 2016. This Olympiad had several events where
students compete individually to show their skills and
knowledge.
After a successful contest this ye... | 29,031 |
Olympus Måns
Description:
Your Swedish friend Måns loves to take pictures of himself
with mountaintops (or at least hilltops) in the background.
Måns owns a tripod on which he can mount the camera at a height
of up to $4$ feet. He
wants to include the highest mountaintop in the picture. How
far awa... | 29,032 |
On Average They're Purple
Description:
Alice and Bob are playing a game on a simple connected graph
with $N$ nodes and
$M$ edges.
Alice colors each edge in the graph red or blue.
A path is a sequence of edges where each pair of consecutive
edges have a node in common. If the first edge in the pair is
... | 29,033 |
On-Call Team
Description:
An IT company has formed an on-call team of software
engineers who will manage their backend services and make sure
that these services run without interruption. When services go
down, for each service that is down the on-call team must
dispatch one member who is familiar with... | 29,034 |
Once in a Blue Moon
Description:
Luna and her brother Solomon live very far from each other.
To make sure they still meet now and then Luna has already
booked in a number of days in which she will go and visit
Solomon. The only way for Luna to get to Solomon is by taking
the Orbital. Since Solomon is p... | 29,035 |
One Chicken Per Person!
Description:
Dr. Chaz is hosting a programming contest wrap up dinner.
Dr. Chaz has severe OCD and is very strict on rules during
dinner, specifically, he needs to be sure that everyone take
exactly $1$ piece
of chicken at his buffet, even if that will result in an
enormous ... | 29,036 |
One-Way Roads
Description:
In the ACM kingdom, there are $N$ cities connected by $M$ two-way roads. These cities are
connected, i.e., one can reach from any city $X$ to any other city $Y$ by going through some of these
roads. One day, the government wishes to assign for each road a
direction, such that one... | 29,037 |
Ones
Description:
Given any integer $1 \le
n \le 100\, 000$ not divisible by $2$ or $5$, some multiple of
$n$ is a number
which in decimal notation is a sequence of $1$’s. How many digits are in
the smallest such a multiple of $n$? There are at most
$1000$ test
... | 29,038 |
Onion Primes
Description:
An onion is a vegetable that is well known for its layers
that can be peeled off to reveal … more layers of
onion. This is the inspiration for the idea of an onion
prime,1 which is a prime number with an
analogous layered structure. More precisely, a positive
integer, $n$,... | 29,039 |
Oooh I See
Description:
Captain O’Capten has hidden some treasure and created a map
to mark where it is buried. Rather than using ‘X’ to mark the
spot, he has decided to obfuscate the location by using a grid
of uppercase O (the letter O) characters and 0
(the number 0) characters. The
treasure’s p... | 29,040 |
Oop
Description:
Little Matej is solving an OOP (Object-oriented programming)
laboratory exercise and he’s having trouble with solving one
subtask.
He is given a set that contains $N$ words. He is also given
$Q$ queries where each
query is one pattern. A pattern consists of a single character
“*” ... | 29,041 |
Open Source
Description:
At an open-source fair held at a major university, leaders
of open-source projects put sign-up sheets on the wall, with
the project name at the top in capital letters for
identification.
Students then signed up for projects using their userids. A
userid is a string of lower-ca... | 29,042 |
Open-Pit Mining
Description:
Open-pit mining is a surface mining technique of extracting
rock or minerals from the earth by their removal from an open
pit or borrow. Open-pit mines are used when deposits of
commercially useful minerals or rocks are found near the
surface. Automatic Computer Mining (ACM... | 29,043 |
Opening Ceremony
Description:
For the grand opening of the algorithmic games in
NlogNsglow, a row of tower blocks is set to be demolished in a
grand demonstration of renewal. Originally the plan was to
accomplish this with controlled explosions, one for each tower
block, but time constraints now requir... | 29,044 |
Opportunity Cost
Description:
As with most types of products, buying a new phone can be
difficult. One of the main challenges is that there are a lot
of different aspects of the phone that you might care about,
such as its price, its performance, and how user-friendly the
phone is. Typically, there wil... | 29,045 |
Optimized Cheating
Description:
Bob’s favorite game just released a limited-time item for
sale that will boost his game character’s power significantly.
However, there is not enough time for Bob to acquire sufficient
in-game currency to purchase the item. Bob thus decides to
resort to a cheat tool he f... | 29,046 |
Orangestone Network
Description:
Sensing an opportunity, you decide to become a
telecommunications mogul by connecting $n$ villages with orangestone links.
To save costs, you use the minimum number of links required to
connect all $n$ of the
villages, and since lag would be unbearable otherwise, any tw... | 29,047 |
Ordered Problem Set
Description:
You are running a programming contest that features
$n$ problems of distinct
difficulties. You wish to announce ahead of time that the
problems are ordered in such a way that, if the problems are
divided into $k$ sections
numbered $1$ through
$k$, each with exac... | 29,048 |
Ordering Hotbar
Description:
Dan is an epic gamer attempting his longest speedrun yet.
Before he makes his attempt, he wants to organize his hotbar so
that it is easier to use. The hotbar is a list of items that
are usually displayed on the bottom of the screen that are
available to the player to use t... | 29,049 |
Orderly Class
Description:
Ms. Thomas is managing her class of $n$ students.
She placed all her students in a line, and gave the
$i$-th student from the
left a card with the letter $a_
i$ written on it.
She would now like to rearrange the students so that the
$i$-th student from the
left has a ca... | 29,050 |
Ordinals
Description:
The Von Neumann ordinals are a number system. Ordinal
numbers can be represented as sets of all numbers less than
that number:
## Input
Input consists of a single integer $0 \le n \le 8$.
## Output
The output is the representation of that number as a set as
specified above.
**Sam... | 29,051 |
Ordinary Ordinals
Description:
Sets, sets, sets. Everything in math is just a set. Even the
natural numbers can be represented as sets. For example, we can
represent the the number $0$ as the empty set $\{ \} $. The number $1$ can be represented as $\{ \{ \} \} $.
But what about $2$?
Consider $\{ \{ \} , ... | 29,052 |
Oreperations Research
Description:
You run a massive mining facility that extracts ore from a
mine and loads it onto long trains for shipment to factories
around the nation. A train consists of $n$ cars, where car $i$ has capacity $c_ i$, indicating how many tons of
ore it can carry. Ore is dropped into th... | 29,053 |
Organ-free Man
Description:
Every so often, a shipment of universal robots comes from
Earth to Mars in order to help you with routine colonization
tasks. The robots are called Organ-free Men (precisely
OFMv5001.41.912) and each one of them is identified by a unique
serial number, which is a positive in... | 29,054 |
Organising the Organisation
Description:
I am the chief of the Personnel Division of a moderate-sized
company that wishes to remain anonymous, and I am currently
facing a small problem for which I need a skilled programmer’s
help.
Currently, our company is divided into several more or less
independent... | 29,055 |
Organizator
Description:
Unexpected problems with law enforcement have convinced
Mirko to take up a less lucrative but less morally ambiguous
career: he has become the chief organizer of a team computer
science contest. There are $N$ CS clubs that wish to participate
in the contest.
The presidents of ... | 29,056 |
Origami
Description:
Origami is the old Japanese art of folding single sheets of
paper into the forms of animals, flowers and other figures.
Recently a programmable machine was constructed to make some of
the simpler kinds of origami. This machine has a large board
with coordinate system drawn on it. F... | 29,057 |
Ornaments
Description:
Your task is to write a program that calculates the length
of the string, given the radius $r$ of the circle, the distance
$h$ from the knot to the
center of the circle, and some multiplier to account for the
excess needed to tie the knot.
## Input
The input will contain multip... | 29,058 |
Orphan Backups
Description:
GigantoCorp has a problem. They have removed all tape drives
from their data center and are doing all of their backups to
disk storage. However, they seem to have used more disk space
than their backup software indicates should be in use. They
think that there are files on t... | 29,059 |
Ortest Path
Description:
Consider an undirected graph where each edge $e$ is labelled by a truth value
$b(e)\in \{ 0,1\} $, where
we interpret $0$ as false
and $1$ as true. An
ortest path is a simple path whose disjunction
(Boolean “or”, $\vee $) is
$1$, i.e., where
$b(v_1v_2) \vee \dots \v... | 29,060 |
Orthogonal Rotation
Description:
You are given two vectors $v_1, v_2$ of the same length
$n$. You need to make them
fit together, which means that they have to be orthogonal to
one another. Possibly they fit together from the start, but if
not we can amend this. We can rotate $v_2$, meaning that we can... | 29,061 |
Orðla
Description:
After each guess the computer gives some hints by colouring
the letters of the guess word, the colours signifying how close
the word is to the secret word. The computer colours the
letters in the following way:
* Letters that match the corresponding letters in the
secret word ar... | 29,062 |
Other Side
Description:
John Doe wants to transport his possessions from one bank of
Lake Michigan to the other. His possessions consist of
$W$ wolves, $S$ sheep, and $C$ cabbages. The transportation will
be carried out using a boat that can hold up to $K$ of these items at the same time.
During each s... | 29,063 |
Otpor
Description:
Mirko has been a very good boy, so he got exactly what he
wanted for his birthday, a “Young physicist” kit! In the kit,
there are $N$ types of
resistors, connecting wires and an ohmmeter. If a resistor is
of type $i$, it provides a
resistance of precisely $R_
i$ ohms.
As we ... | 29,064 |
Out of Context
Description:
It’s that time of year: election season. Political speeches
abound, and your friend the armchair pundit likes to find
quotes of politicians and use them out of context. You want to
help your friend by developing a method to search through text
for specified patterns.
One of... | 29,065 |
Out of Sorts
Description:
Ann Logan is fascinated with finite sequences of integers.
She is particularly interested in sequences of the form
$x_1, x_2, \ldots , x_ n$
where:
* $x_{i} = (ax_{i-1}+c)\mod
m$,
* $n$, $m$, $a$, and $c$ are positive integer
constants,
* $x_0$ is a
non-... | 29,066 |
Outer Space Invaders
Description:
The aliens from outer space have (finally!) invaded Earth.
Defend yourself, or be disintegrated! Or assimilated. Or eaten.
We are not yet sure.
The aliens follow a known attack pattern. There are n
attackers, the $i$-th one
appears at time $a_ i$, at
distance $d_ ... | 29,067 |
Outing
Description:
Organising a group trip for the elderly can be a daunting
task... Not least because of the fussy participants, each of
whom will only make the trip on condition that some other
participant also comes.
After some effort, you have taken from each of your
participants a number, indica... | 29,068 |
Outsourcing
Description:
Mr. Cooper is a manufacturer of science fiction action
figures and he thinks that his local factory causes too many
costs. He once heard of certain foreign countries where workers
are much less expensive and also more dedicated. So he decided
to look for an available action fig... | 29,069 |
OvalWatch
Description:
It’s the year 2020 and OvalWatch is the most popular massive
online first person shooter game.
OvalWatch features a set of $N$ characters, and during a match,
each player can choose one of these characters to play.
In order to keep each match interesting, for every match,
OvalWatch... | 29,070 |
Over the Hill, Part 1
Description:
Hill encryption (devised by mathematician Lester S. Hill in
1929) is a technique that makes use of matrices and modular
arithmetic. It is ideally used with an alphabet that has a
prime number of characters, so we’ll use the $37$ character alphabet A, B, $\ldots $, Z,
... | 29,071 |
Over the Hill, Part 2
Description:
Bob Roberts is part of a crack espionage team working for
the CIA (Chocolate Institute of Alabama) and he is working on
decrypting the encoded messages of their arch rivals at the NSA
(Nougat Society of Arkansas). Fortunately, the NSA’s espionage
staff is not nearly a... | 29,072 |
Overdraft
Description:
Banks often charge overdraft fees if you attempt to withdraw
more money from your account than is available in your current
balance. Given a sequence of deposits and withdrawals (and
assuming each deposit and withdrawal is immediately reflected
in your balance), determine the min... | 29,073 |
Overlapping Maps
Description:
Fred and Sam are traveling together. Both have maps of the
area. The maps cover exactly the same territory, and have
exactly the same ratio of width to height, but Sam’s is at a
smaller scale than Fred’s, so it’s a bit smaller. Fred puts his
map on a table. Sam throws his ... | 29,074 |
Ozljeda
Description:
Due to the frantical usage of the racket to kill flies,
Marin has sustained a serious bodily injury known to the
medical community as epicondylitis lateralis humeri. His
grandma has advised smearing rakija over it, the doctor has
prescribed a strong painkiller, but Marin has ignore... | 29,075 |
PUBNite
Description:
Recently, Anthony has really gotten into the battle royale
games. His favorite game is PUBNite.
In PUBNite, many players fight against each other and try to
be the last one alive. One of the most well-known mechanics in
PUBNite is the safety zone, which is a circular area. Players
... | 29,076 |
Pachinko
Description:
You have been hired by Addictive Coin Machines to help
design the next hit in their line of eye-catching,
coin-guzzling, just-one-more-try Pachinko machines for casinos
around the world.
Playing a Pachinko machine involves launching balls into a
rectangular grid filled with pegs,... | 29,077 |
Pachinko Probability
Description:
A pachinko machine is a Japanese invention that is sort of
like a pinball machine. Each pachinko machine uses marbles
which fall from the top and bounce off of fixed pins until they
reach the bottom. When they reach the bottom, if they fall into
a particular area (a ‘g... | 29,078 |
Pachyderm Peanut Packing
Description:
You are an elephant working for peanuts. The job that you do
is to walk around the packing plant and make sure that peanuts
are being packed correctly. Peanuts at your plant are packed by
size — small, medium, and large. You walk around and note every
peanut that i... | 29,079 |
Packagemanager
Description:
Doris has started her work as a packagemanager at the Pacman
company (a part of the Sudo group). Her job is to make sure
each of their stores has the most recent model of envelope,
cardboard box, etc. Doris would however like to automate this
task.
She has a list of all typ... | 29,080 |
Packing Pests
Description:
You are an employee #333-4-591032 at a candy sorting
company. Your job is simple. $N$ candies, of $M$ different colors, will be thrown
in your direction, one at a time. The $i^\text {th}$ thrown candy will have
color $C_ i$ and value
$V_ i$. Each time, you
must either swa... | 29,081 |
Padel Prize Pursuit
Description:
There are $N$
participants numbered $0$
to $N-1$ competing in a
padel tournament held over $M$ days. Exactly one match is held
each day. There are $M$
medals handed out in the tournament, a new one for each match.
In the match on day $i$
$(0 \le i \le M-1)$, the... | 29,082 |
Page Layout
Description:
When you are designing a complicated document, page layout
is important. Newspapers and magazines don’t just put a whole
bunch of text that covers the page left-to-right, listing one
article after another. They put multiple articles on a page, at
different positions designed to... | 29,083 |
Paint
Description:
You are painting a picket fence with $n$ slats, numbered from $1$ to $n$. There are $k$ painters willing to paint a
specific portion of the fence. However, they don’t like each
other, and each painter will only paint their given portion of
the fence if no other painter overlaps their por... | 29,084 |
Paint Buckets
Description:
Gladys runs a paint shop with a huge stock of paint buckets
of various volumes and hues. One of the special features of her
shop is that she takes orders of any of the
$10^9$ colors there are.
On the surface of things, this cannot be possible – of course,
there is not spa... | 29,085 |
Paintball
Description:
Marek and his schoolmates have just finished their studies
at the university. They wanted to celebrate it with a game of
paintball. After an hour of playing a very strange thing
happened – everyone had exactly one bullet left. Marek, being a
very curious person, wanted to know wh... | 29,086 |
Paintball II
Description:
You are playing paintball on a $1000\times 1000$ square field. A
number of your opponents are on the field hiding behind trees
at various positions. Each opponent can fire a paintball a
certain distance in any direction. Can you cross the field
without being hit by a paintball... | 29,087 |
Painted Corridors
Description:
The Institute of Colorfully Painted Corridors is planning
the construction of a new building. The building has numerous
junctions, and corridors that each connect a pair of junctions.
The corridors will be painted by amazing new painting robots
that drive along the corrid... | 29,088 |
Painting a Fence
Description:
You need to hire some people to paint a fence. The fence is
composed of $10\, 000$
contiguous sections, numbered from $1$ to $10\, 000$.
You get some offers from painters to help paint the fence.
Each painter offers to paint a contiguous subset of fence
sections in a part... | 29,089 |
Paintings
Description:
Catherine recently got into painting minimalist art. For her
next painting she wants to create an image with $N$ vertical strips of distinct
colors. She always begins painting her vertical strips on the
left side of the canvas and proceeds to the right side.
However, there are ce... | 29,090 |
Paired Furnaces
Description:
Just outside the entrance to your mine shaft you have a row
of $n$ furnaces; some of
them are on and some are off. Unlike regular furnaces, these
furnaces can only be turned on in neighboring pairs. In one
move you can either choose two neighboring furnaces which are
on... | 29,091 |
Pairing Socks
Description:
Being a computer scientist, her mother finds this a fair
objection. Looking over her list of potential chores, she
picked one she thinks should be easy to solve – pairing a
number of different kinds of socks.
In the beginning, there are $2n$ socks stacked in a pile. To pair
... | 29,092 |
Palačinke
Description:
Ana has a couple of classmates coming over for crêpes (known
as palačinke in Croatian). They are coming in $T$ minutes, and Ana just found out
that she has neither one of the four required ingredients
(flour, milk, eggs and jam). She hops into her car and drives
around her neighb... | 29,093 |
Paleta
Description:
Little Mirko spends his free time painting. For this hobby,
he likes to use brushes and a palette containing $K$ colors overall. His friend Slavko
decided to use Mirko’s talent and gave him his new coloring
book for Mirko to color. The coloring book contains
$N$ images numbered
... | 29,094 |
Palindrome Names
Description:
Anna and Bob are having a baby. They both enjoy the
advantage of having palindrome names, meaning that their names
are spelled the same way forwards and backwards. Wanting to be
good parents, they decide to give their child a palindrome name
too. The only problem is that t... | 29,095 |
Palindrome Substring
Description:
A palindrome is a word or phrase that reads the same
backwards or forwards. For this problem, we’re going to find
all the different palindromes that occur inside a string.
We’ll say that string $a$ is a nontrivial
palindrome substring of $b$ if $a$ is a substring of $b$, ... | 29,096 |
Palindrome-Free Numbers
Description:
A string is a palindrome if it remains the same when it is
read backwards. A number is palindrome-free if it does not
contain a palindrome with a length greater than $1$ as a substring. For example, the
number $16276$ is
palindrome-free whereas the number $17276$ is... | 29,097 |
Palindromes
Description:
Sam is starting a new company, and has just chosen its name.
The name is a string $s =
s_1s_2\dots s_ n$ of length $n$. The name is so long that
customers won’t remember the full name. Rather, each customer
is going to remember only a substring $t$ of the full name, and differe... | 29,098 |
Palindromes in crosswords
Description:
Mr. F. just loves palindromes (a palindrome is a word
that reads the same forwards and backwards). He got hold of his
mom’s solved crosswords and now he is looking for palindromes
in them. The crosswords are somewhat unusual: each is an
$n\times n$ grid with no
... | 29,099 |
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