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Colorful Trees Description: Given a tree with colored vertices, for each edge, how many pairs of vertices with the same color have that edge on the path between them? Note that since it’s a tree, each pair of nodes has exactly one path between them. ## Input The first line of input contains a single inte...
26,900
Coloring Graphs Description: There is one problem, as you can imagine: there is no money to train teachers to grade these students’ submissions! Thus, your task is to write a program that computes the sample solutions for the graphs given on each work sheet! ## Input The input consists of a description o...
26,901
Coloring Socks Description: Having discolored his white socks in a rather beige shade (as seen on the picture), Luktas Svettocek realised he can’t just throw all his laundry into one machine and expect it to retain its original colors. However, he is also too lazy to do his laundry in several rounds. H...
26,902
Colorland Description: Yancy is designing a new board game called Colorland. The rules of Colorland are as follows: * Colorland’s board is a linear sequence of $N+1$ squares. The first square is a special start square, the remaining $N$ squares are colored blue, orange, pink, green, red, or yellow...
26,903
Colosseum of Fools Description: Deep in the caverns of a fallen kingdom, lies a sacred battleground for warriors all across the lands to test their skills. Tonight, $b$ bugs have come to the arena to challenge the trials the Colosseum holds. To assist them in their battles, each bug wields several ...
26,904
Colour Wars Description: A school is having a vote in what their primary school colour should be. While counting the votes, the principal of the school accidentally lost count of how many students there were. He then asked $N$ distinct students “How many other students voted for the same colour as ...
26,905
Colourful Graph Description: Consider an undirected graph on $n$ vertices. A $k$-colouring of the graph is simply an assignment to each vertex one of the $k$ colours. There are no other restrictions – two vertices can get the same colour even if they are connected by an edge. You are given two $k$-colouri...
26,906
Colourful New World Description: You may be familiar with the philosophical thought experiment referred to as Mary’s Room. If not, it goes as follows: Mary is a scientist who has lived in a black and white room her entire life. She has also spent her whole life studying biological colour perception an...
26,907
Colouring Book Description: The Ministry of Trigonometric Artistry (or MTA for short) is producing a colouring book to get children interested in trigonometry at a young age. The colouring book consists of many pages. On each page is a set of numbered dots that are to be connected with straight line se...
26,908
Combination Lock Description: Now that you’re back to school for another term, you need to remember how to work the combination lock on your locker. A common design is that of the Master Brand, shown at right. The lock has a dial with $40$ calibration marks numbered $0$ to $39$ with $0$ at the top and ...
26,909
Combinatorial Stanley Cup Description: You have always dreamt to get your name on the Stanley Cup, but you have never played hockey. A friend of yours heard of an alternative: the Combinatorial Stanley Cup! If you solve a single programming problem, you will get your name on this purely fictional troph...
26,910
Comma Sprinkler Description: Dr. Sprinkler’s rules for adding commas to an existing piece of text are as follows: * If a word anywhere in the text is preceded by a comma, find all occurrences of that word in the text, and put a comma before each of those occurrences, except in the case whe...
26,911
Commemorative Race Description: Filiberto is planning a race to celebrate the 2019 ICPC Mid-Central Regional. The racers compete by going down a mountain on a set of roads. As it would be dangerous to have cars speeding at each other in opposite directions, racers may only drive downhill on each road i...
26,912
Committee Assignment Description: You are the chair of a large department, and, as such, it’s your job to assign department members to committees. Everyone has to be on exactly one committee, but some department members don’t get along and cannot be assigned to the same committee. Of course, you would ...
26,913
Common Factors Description: Everyone likes to share things in common with other people. Numbers are the same way! Numbers like it when they have a factor in common. For example, $4$ and $6$ share a common factor of $2$, which gives them something to talk about. For a given integer $n$, we define...
26,914
Common Ground Description: Quibble Pants recently met his “special somepony” Clear Sky. To get closer to her, he wants to spend some quality time together with her daughter, Wind Sprint. Unfortunately, while Wind Sprint is a huge sportspony, Quibble is anything but. Today, in an attempt to find some c...
26,915
Common Subexpression Elimination Description: Let the set $\Sigma $ consist of all words composed of 1–4 lower case letters, such as the words “a”, “b”, “f”, “aa”, “fun” and “kvqf”. Consider expressions according to the grammar with the two rules for every symbol $f \in \Sigma $. Any expression ca...
26,916
Communicating The Strategy Description: This is an interactive problem. During a Pokenom battle, a Pokenom trainer must come up with a strategy and communicate the strategy to his Pokenom in a very efficient way. To become the best Pokenom trainer, Bash is practicing how to communicate the strategy to hi...
26,917
Communication Line Description: This problem requires you to write a program which does three tasks which might facilitate the use of a communication line. The first task is that of translating from one set of codes to another. The second task is to compress 80-character lines to a smaller size by comp...
26,918
Communication Matters Description: Satsuki and Mei both have to guess a secret number. Satsuki is trying to guess $a$ and Mei is trying to guess $b$. Both $a$ and $b$ can take values between $1$ and $n$. Satsuki and Mei know the joint probabilities of their secret numbers being a specific number. ...
26,919
Communications Satellite Description: The Johnson Space Center has hired you to design NASA’s new communications satellite! The satellite, consisting of a set of dish antennas held together with titanium beams, must meet NASA’s exacting specifications, but a lot of the design is up to you. Specificall...
26,920
Company Picnic Description: Each year, your employer hosts a company picnic. This event features a three-legged race, a race where two runners work as a team, running side-by-side with the legs between them tied together. It is more difficult to run like that, so teams run at a speed that is the minimu...
26,921
Comparator Description: Many programming languages let you define custom comparators to sort user-defined objects. IFFY is a programming language where the only programs are functions intended to be comparators. These functions operate on bitstrings, hereafter called “words”. Words are 1-indexed start...
26,922
Comparing Answers Description: In a place in Southwestern Europe, the name of which I do not wish to recall, not long ago there were $n$ cities connected by unidirectional roads, with possibly more than one road connecting a city to another one, or even to itself. As a homework assignment for your geog...
26,923
Compass Card Sales Description: To decide how unique a card is in the deck, she proceeds as follows. For each of the three colors she finds the closest other card in both directions, and then computes the angle between these two other cards. For instance if she has three cards with red angles $42$, $90...
26,924
Compensation Description: In the free-market, ruthlessly capitalist world of train fares, only one thing matters: incentives. Train companies are incentivised with bonuses for high throughput, successful journeys, and customer satisfaction. Conversely, the companies are disincentivised from failure via ...
26,925
Competitive Arcade Basketball Description: You’re attending a arcade basketball competition, where the objective is to score as many points as possible until the time runs out. The announcer has informed the crowd that their scoreboard is broken, so they don’t have a way to keep track of all the scores...
26,926
Compiler Description: One thing almost all computers have in common, whether it is a simple stack-based calculator, a 6502 powered BBC Micro, or a brand new Android phone, every modern computer requires programs that turn either high-level languages or assembly language into machine code. UKIEPC recen...
26,927
Completing the Square Description: In the heart of your home city, there is an old square, close to the train station, appropriately called Station Square. It used to look like a perfect square: four sides of equal length joined by right angles. However, it hasn’t looked like this for decades, as one o...
26,928
Composed Rhythms Description: Rhythm is an important part of music and it is crucial for aspiring musicians to gain understanding of it. As the skill of the musician advances, more complex rhythms are introduced to them. To ease the learning of musical passages, a method of simplifying rhythms can be h...
26,929
Compositions Description: A composition of an integer $n$ is an ordered set of integers which sum to $n$. Two compositions with the same elements but in different orders are considered different (this distinguishes compositions from partitions). For example, all the compositions of the first fe...
26,930
Compound Words Description: Write a program that reads a list of words from standard input and prints out a sorted list of all unique compound words that can be made by concatenating two different words from the input list. If the same compound word can be formed more than one way, it should only be li...
26,931
Compression Description: You have a list $x_1,\dots ,x_ N$ of natural numbers and would like to encode it in a particular compressed format while minimizing the size of the compressed file. The compressed format consists of a string of bits (0 or 1), which is divided into contiguous blocks of varia...
26,932
Compression Description: If there are multiple choices of repeating consecutive substrings to remove, DRY should choose in a way that results in the shortest possible final string. For example, in the string “ABBCDCABCDCD”, DRY has two choices — either removing the repeated “B” near the beginning, or t...
26,933
Concentration Description: Concentration is a not so popular 2 player card game of both skill and luck. The standard Concentration game is played with one or two 52-card decks, however, for the sake of the problem, we will look at a variation of Concentration. The rules are as follows: * A card is repres...
26,934
Concert Rehearsal Description: A class of $n$ music students are going to rehearse for a concert in a recital hall. In one rehearsal pass, each student will give one performance in order from student $1$ to student $n$. Student $i$’s performance has a duration of $d_ i$. After the last stud...
26,935
Condorcet Description: Consider an election where there are some candidates, one winner, and each voter has a complete ranked preference of the candidates. One possible method of determining the winner is to examine each pair of candidates and see which would win in a head-to-head matchup (i.e., which ...
26,936
Confined Catching Description: You are playing a board game against an AI on a square grid consisting of $n\times n$ cells. You have two game pieces and the AI has one, and each piece is placed in one of the grid cells. Your goal is to “catch” the AI’s piece, that is, one (or both) of your pieces h...
26,937
Conformity Description: Frosh commencing their studies at Waterloo have diverse interests, as evidenced by their desire to take various combinations of courses from among those available. University administrators are uncomfortable with this situation, and therefore wish to offer a conformity prize to...
26,938
Conga Line Description: There’s currently a dance party being held in a nondescript location. The party is joined by $N$ couples. To liven up the party, the host, who is not dancing, has decided to perform a conga line. As such, the host asks all the couples to stand in one line. At first, each couple...
26,939
Connect Description: When constructing electric circuits one has to connect pairs of points using wire, preferable as short as possible. In this problem we have an empty circuit board of size $N \times M$ where we want to connect the two points $A_1$ and $A_2$ with each other using one wire, and th...
26,940
Connect Five Description: In the town of Nattanham, all roads run either north to south, or east to west, and span the entire town. Furthermore, all roads are an equal distance apart. This makes navigating the town extremely easy. Unfortunately, the roads are quite poor and could do with a fresh layer...
26,941
Connect the Dots Description: Write a program to read in a visual description of a connect-the-dots puzzle, then connect the dots and print the result. ## Input Input contains up to $100$ images. Each image is rectangular and has dots indicated by the symbols $0, 1, \ldots , 9$, a, b, …, z, A, B, …, ...
26,942
Connect the Dots Description: A famous logical problem is that of connecting 9 dots on a paper by drawing 4 line segments with a pencil, while never lifting the pencil from the paper. While this is easy enough (although it requires some thinking outside of the box), Simone has recently been building a ...
26,943
Connect-N Description: A popular connection game that is well-known around the world is Connect Four. In this two-person game, each player is assigned a colored disc (red or blue) and takes turns dropping one of their colored discs from the top into a seven-column, six-row vertically upright game board...
26,944
Connectedness Description: You are given an undirected graph $G=(V,E)$. If you are drawing in the edges one by one, how many edges did you add when the graph becomes connected for the first time. If the graph never becomes connected after drawing all the edges, output -1. Here are some useful definition...
26,945
Connecting Computers Description: The tech team is gearing up for the PacNW Regional! There are $n$ computers that need to be connected together for the contest, isolated from the outside internet. There are $m$ bidirectional connections between computers, each connection requiring one of $k$ different...
26,946
Conquer The World Description: Bwahahahahaha!!! Your nemesis, the dashingly handsome spy Waco Powers, has at last fallen to your secret volcano base’s deathtraps (or so you assume, being a little too busy to witness it firsthand). At long last, you are all set to Conquer The World! Nothing will stand ...
26,947
Conquest Description: Nomads, Kingdoms, and Tribes are on the islands of the great seas. Bridges span between islands allowing travel between them. It is possible to get from every island to every other island through some sequence of bridges. The islands were at peace until everything changed when the...
26,948
Conquest Campaign Description: Since the beginning of $30$-th century, the Country of Circles has become the strongest country in the world. To expand its territory to the west, they plan to invade the Country of Rectangles. The territory of the Country of Rectangles is represented by a $R \times C$ t...
26,949
Consecutive Prime Sums Description: You are given a positive integer $n$ and should print the prime number $< n$ that can be written as the sum of the greatest number of consecutive primes. For example $41$ can be written as $2 + 3 + 5 + 7 + 11 + 13$ and it can be seen that $41$ is the prime $< n$...
26,950
Conservation Description: The most famous painting in Byteland—a portrait of a lady with a computer mouse by Leonardo da Bitci—needs to be conserved. The work will be conducted in two narrowly specialized laboratories. The conservation process has been divided into several stages. For each of them, we ...
26,951
Constellation Creation Description: As you journey further into space, the relative positions of the stars have shifted so much that you can no longer recognize the constellations that you’ve learned about growing up. This makes for a great opportunity – now you can come up with your own constellations...
26,952
Constrained Freedom of Choice Description: You live in a rectangular grid of ASCII characters. Your home is in the lower left corner and you work in the upper right corner. Sidewalks look like periods (.) and buildings, cars, trash cans and other obstacles look like pound signs (#). You walk to work ea...
26,953
Construction Toy Description: Alaa fondly remembers playing with a construction toy when she was a child. It consisted of segments that could be fastened at each end. A game she liked to play was to start with one segment as a base, placed flat against a straight wall. Then she repeatedly added on tria...
26,954
Construction Worker Description: To build the tallest tower, SoCCat needs a lot of cat dollars. SoCCat plans to make money by taking on construction jobs optimally. There are $n$ companies that periodically offer construction jobs every $T$ cat days. Company $i$ offers a construction job at the beginn...
26,955
Consulting Gigs Description: In the computer-generated world Matriks, you work as a consultant for some hip IT companies that need unique slides for their cool office spaces. During the past year, you got a number of job offers at different points in time, measured in milliseconds since the start of th...
26,956
Contact Tracing Description: A deadly virus is sweeping across the globe! You are part of an elite group of programmers tasked with tracking the spread of the virus. You have been given the timestamps of people entering and exiting a room. Now your job is to determine how the virus will spread. Hurry u...
26,957
Contact Tracing Description: A novel infectious disease has started spreading through the population. You are tasked with figuring out who might be infected in order to get them to quarantine. The behavior of the disease among members of the population is as follows: * When a person comes into contact wit...
26,958
Containment Description: A $10 \times 10 \times 10$ three-dimensional grid of tightly packed cubic atomic energy cells aboard the starship Fiugtuwf is reporting failures on several of its cells. The ship’s engineer must set up enclosures that will contain all of the cells that are reported to be fa...
26,959
Contest Advancement Description: You are the RCD for your regional contest. It just ended and you now need to decide which teams qualify for the next level of competition. The teams are uniquely ranked (there are no ties). The next level has a limit on how many teams from any given school can participa...
26,960
Contest Construction Description: The ICPC NAC staff have written a number of problems and wish to construct a problem set out of them. Each problem has a positive difficulty rating. A contest has a Nice difficulty distribution if, when the difficulties of the problems are sorted in ascending order, e...
26,961
Contest Struggles Description: She recalls hearing the judges talk about the difficulty of the problems, which they rate on an integer scale from $0$ to $100$, inclusive. In fact, one of the judges said that “the problem set has never been so tough, the average difficulty of the problems in the pro...
26,962
Contingency Planning Description: Taking that internship in a remote mountain may not have been the best idea. Pulling that lever with the skull symbol just to see what it did was not so smart either. But now is not the time for regrets because you need to find a way to prepare for these mutant zombies...
26,963
Continued Fraction Description: where $a_0, a_1, a_2, \dots $ are integers and $a_1, a_2, \dots > 0$. We call the $a_ i$-values partial quotients. For example, in the continued fraction representation of $5.4$, the partial quotients are $a_0 = 5, a_1 = 2, a_2 = 2$. This representation of a real num...
26,964
Continuous Median Description: In Statistics, the median of an array $\textbf{A}$ of $\textbf{N}$ integers is a value which divides array $\textbf{A}$ into two equal parts: the higher half and the lower half. In the case when $\textbf{N}$ is odd, the median is clearly defined: the middle value of the ...
26,965
Conversation Log Description: Popular social networking site My+Din is struggling to manage its many popular forums. Recent regulation requires the site to report users engaged in conversations about certain topics. The sheer number of users means manual monitoring is too costly and so the site has ask...
26,966
Converting Romans Description: The Roman numerals are a numeral system that originated in ancient Rome and was widely used throughout Europe well into the Late Middle Ages. It differs from the Arabic system that we mostly use today in that numbers are written with combinations of letters from the Latin...
26,967
Convex Contour Description: A number of geometric shapes are neatly arranged in a rectangular grid. The shapes occupy consecutive cells in a single row with each cell containing exactly one shape. Each shape is either: * a square perfectly aligned with the grid square, * a circle inscribed in the grid sq...
26,968
Convex Hull Description: ## Input Input contains several test cases. Each test case begins with an integer $n$ ($1 \leq n \leq 10000$). Then follow a list of $n$ points, one per line, each of the form $x\ y$. Coordinates are integer with absolute value bounded by 10000. The input is terminated by ...
26,969
Convex Hull Description: Finding the convex hull of a set of points is an important problem that is often part of a larger problem. There are many algorithms for finding the convex hull. Since problems involving the convex hull sometimes appear in the ACM World Finals, it is a good idea for contestants...
26,970
Convex Hull Extension Description: Dr. Hugh Klidd is a geometry expert who has recently become preoccupied with convex hulls. Recall that for a set of points in the $x\textrm{-}y$ plane, the convex hull is the smallest convex polygon containing all of those points. (A convex polygon has the propert...
26,971
Convex Polygon Area Description: For this problem, you just need to be able to calculate the area of convex polygons. ## Input Input starts with an integer $1 \le n \le 100$, indicating the number of convex polygons. The next $n$ lines each contain one convex polygon description. Each begins with an inte...
26,972
Conveyor Belts Description: Your factory has $N$ junctions (numbered from $1$ to $N$) connected by $M$ conveyor belts. Each conveyor belt transports any product automatically from one junction to another junction in exactly one minute. Note that each conveyor belt only works in one direction. There can...
26,973
Conveyor Belts Description: You are an employee of the Boxing And Processing Company and you are tasked with distributing boxes in one of the company’s enormous warehouses. At BAPC Ltd., boxes travel by conveyor belt. Two conveyor belts can be merged into one by letting one drop its content onto the ot...
26,974
Convoy Description: You and your friends have gathered at your house to prepare for the Big Game, which you all plan to attend in the afternoon at the football stadium across town. The problem: you only have $k$ cars between you, with each car seating five people (including the driver), so you migh...
26,975
Cookie Cutter Description: Everyone loves chocolate chip cookies! Which unfortunately means sharing sometimes. In this case, you have generously agreed to split a square chocolate chip cookie with your friend. Because it is your cookie, you get to choose how to cut the cookie, and which piece to give ...
26,976
Cookie Cutters Description: Theta likes to bake cookies for the upcoming holidays. She has a selection of cookie cutters of different shapes and sizes. She thinks it’s unfair that some shapes are larger than others – because even if everyone gets the same number of cookies, some will end up with more d...
26,977
Cookie Game Description: Gustav and Oskar found some cookies in the base, so they put them in a line on the table and numbered them $1$ to $n$ from left to right. Cookie number $i$ takes $a_ i$ bites to eat. Gustav and Oskar want to eat the cookies, but they couldn’t agree on how to divide the cookies ...
26,978
Cookie Selection Description: As chief programmer at a cookie production plant you have many responsibilities, one of them being that the cookies produced and packaged at the plant adhere to the very demanding quality standards of the Nordic Cookie Packaging Consortium (NCPC). At any given time, your ...
26,979
Cookies Description: Ann Britt-Caroline has $N$ different types of cookies. She has $A_ i$ cookies of type $i$. Now, Ann is wondering how many cookies she has in total. ## Example In this example, we have $N = 3$ different types of cookies. The number of cookies of each type is $3, 1, 5$. As...
26,980
Cooking Water Description: “A watched pot never boils”, as the saying goes. Chef Edward has been cooking for ages, and empirically the saying seems to be true in his kitchen – he has yet to see a pot actually start boiling. His wife Gunilla is a bit suspicious of Edward’s claim though. She knows how he...
26,981
Cop and Robber Description: In the city of Bytemore crime level is hitting an all–time high. Among other misdemeanours, robberies are happening every day. And when the crime is committed, it is always up to a lone patrolling police officer to chase down the robber through the narrow alleys that connect...
26,982
Coprime Integers Description: Given intervals $[a, b]$ and $[c, d]$, count the number of ordered pairs of co-prime integers $(x, y)$ such that $a \le x \le b$ and $c \le y \le d$. Coprime integers have no common factor greater than $1$. ## Input The input consists of a single line of four spa...
26,983
Cops and Robbers Description: The First Universal Bank of Denview has just been robbed! You want to catch the robbers before they leave the state. The state of Calirado can be represented by a rectangular $n$-by-$m$ grid of characters, with the character in each grid cell denoting a terrain type. The ...
26,984
Copycat Catcher Description: Code consists of tokens separated by spaces. Tokens are strings of alphabetical letters, numerals, and brackets. If a token consists of only a single alphabetical letter (upper or lowercase), it is a variable in the code. The GCPC wants the plagiarism checker to compare query ...
26,985
Copying DNA Description: Evolution is a seemingly random process which works in a way which resembles certain approaches we use to get approximate solutions to hard combinatorial problems. You are now to do something completely different. Given a DNA string $S$ from the alphabet {A,C,G,T}, find the ...
26,986
Cordon Bleu Description: A Parisian entrepreneur has just opened a new restaurant “Au bon cordon bleu”, named after a famous French recipe. However, no one has any idea of which wine would be appropriate with such a dish. The entrepreneur plans to sample many different wines in order to build the wine ...
26,987
Cornhusker Description: Corn farmers need to do pre-harvest yield estimates to determine the approximate number of bushels of corn their farm will produce. They do this to determine if they have enough storage space (grain bins) to store the harvested crop or if they’ll have to store the corn elsewhere...
26,988
Corrupt Judge Description: You are organising a programming competition in which the rank of a team is first determined by how many problems they have solved. In case of a tie, the team with the lowest time penalty is ranked above the other. However, contrary to the UKIEPC, the time penalty is equal to...
26,989
Cosmic Path Optimization Description: Your long journey through the cosmos has begun, and you have many stops along the way. This journey will take generations, so you need to find the most efficient route from Earth, located at intergalactic coordinates $(X_0, Y_0, Z_0)$, to each of the $N$ planets, a...
26,990
CosmoCraft Description: In the two-player game CosmoCraft you manage an economy in the hopes of producing an army capable of defeating your opponent. You manage the construction of workers, production facilities, and army units; the game revolves around balancing the resources you allocate to each. The...
26,991
Cost of Living Description: A newspaper columnist recently wrote a column comparing Disneyland’s price increases to other things in the economy; e.g., If gasoline were to have increased at the same rate as Disneyland’s admission since 1990, it would cost $\$ 6.66$ per gallon. Consider the prices of a numb...
26,992
Costly Contest Description: The company Mindsight is holding a programming contest for $n$ contestants of varying ages. It has been decided that the contest will be separated into $k$ age divisions. The duration of the contest will be $t$ minutes, the same for all divisions. Mindsight has created a...
26,993
Costume Contest Description: Everyone knows that the highlight of Halloween at HiQ is their annual costume contest. In their costume contest, they have $D$ categories of costumes that they give a “best of” award to, such as most malignant mummy, most ghoulish ghost and most wicked witch. Judges are...
26,994
Councilling Description: Each resident of a particular town is a member of zero or more clubs and also a member of exactly one political party. Each club is to appoint one of its members to represent it on the town council so that the number of council members belonging to any given party does not equa...
26,995
Count Doubles Description: Given an array of $n$ positive integers and an integer $m$, count how many contiguous subarrays of exactly $m$ elements have two or more even values. For example, given the subarray 1 2 3 4 5 6 7 8 and $m = 3$, the three subarrays 2 3 4, 4 5 6, and 6 7 8 each have at...
26,996
Count the Vowels Description: Given a line of text, count the vowels! For this problem, the only vowels are A, E, I, O and U, both upper and lower case. No other letters will be considered vowels for the purposes of this problem. ## Input The single line of input contains a single string $s$ ($1 \le ...
26,997
Count von Walken's Fence Description: The old Count von Walken ponders along the fence of his backyard. The fence has a repeating pattern with poles in the ground at equal distances. Since von Walken has nothing better to do, he counts the number of steps he takes between each pole. The distance betwe...
26,998
Countdown Description: The “Countdown” TV show has a part that consists of obtaining a number by combining six different numbers using the basic mathematical operations: addition, subtraction, product and division. The basic rules for the game are: * The contestant selects six of twenty-four shuffled ...
26,999