Two children take turns breaking up a rectangular chocolate bar 6 squares wide by 8 squares long. They may break the bar only along the divisions between the squares. If the bar breaks into several pieces, they keep breaking the pieces up until only the individual squares remain. The player who cannot make a break loses the game. Who will win?⚡aFirst playerbSecond PlayercIt will be a tie
Question
Two children take turns breaking up a rectangular chocolate bar 6 squares wide by 8 squares long. They may break the bar only along the divisions between the squares. If the bar breaks into several pieces, they keep breaking the pieces up until only the individual squares remain. The player who cannot make a break loses the game. Who will win?⚡aFirst playerbSecond PlayercIt will be a tie
Solution
Para resolver este problema, debemos analizar la cantidad de movimientos posibles y cómo se desarrollará el juego.
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Inicialmente, tenemos una barra de chocolate de 6x8, lo que significa que hay 48 cuadrados en total.
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Cada vez que un jugador hace una ruptura, el número total de piezas aumenta. Por ejemplo, si se rompe la barra en dos partes, ahora hay dos piezas en lugar de una.
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El objetivo del juego es que el jugador que no pueda hacer una ruptura pierde. Esto significa que el juego termina cuando todas las piezas son cuadrados individuales.
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Número de movimientos necesarios: Para que todas las piezas sean cuadrados individuales, necesitamos hacer 47 rupturas (porque empezamos con una pieza y terminamos con 48 piezas, así que 48 - 1 = 47).
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Turnos alternados: Los jugadores se alternan en cada turno. Si hay 47 movimientos en total, el primer jugador hará el primer movimiento, el tercer movimiento, el quinto movimiento, y así sucesivamente. El segundo jugador hará el segundo movimiento, el cuarto movimiento, el sexto movimiento, y así sucesivamente.
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Determinación del ganador: Dado que hay un número impar de movimientos (47), el primer jugador hará el primer y el último movimiento. Por lo tanto, el segundo jugador será el que no pueda hacer una ruptura en su turno final.
Conclusión: El primer jugador ganará el juego.
La respuesta correcta es: a) Primer jugador
Similar Questions
Two children, Lily and Ron, want to share a chocolate bar. Each of the squares has an integer on it.Lily decides to share a contiguous segment of the bar selected such that:The length of the segment matches Ron's birth month, and,The sum of the integers on the squares is equal to his birth day.Determine how many ways she can divide the chocolate.
Alice and Bob are very good friends and they always distribute all the eatables equally among themselves.Alice has 𝐴A chocolates and Bob has 𝐵B chocolates. Determine whether Alice and Bob can distribute all the chocolates equally among themselves.Note that:It is not allowed to break a chocolate into more than one piece.No chocolate shall be left in the distribution.Input FormatThe first line of input will contain an integer 𝑇T — the number of test cases. The description of 𝑇T test cases follows.The first and only line of each test case contains two space-separated integers 𝐴A and 𝐵B, the number of chocolates that Alice and Bob have, respectively.Output FormatFor each test case, output on a new line YESYES if Alice and Bob can distribute all the chocolates equally, else output NONO. The output is case insensitive, i.e, yesyes, YeSYeS, yESyES will all be accepted as correct answers when Alice and Bob can distribute the chocolates equally.Constraints1≤𝑇≤10001≤T≤10001≤𝐴,𝐵≤1051≤A,B≤10 5 Sample 1:InputOutput41 11 31 21 4YESYESNONOExplanation:Test case 11: Both Alice and Bob already have equal number of chocolates, hence it is possible to distribute the chocolates equally among Alice and Bob.Test case 22: If Bob gives one of his chocolates to Alice, then both of them will have equal number of chocolates, i.e. 22. So, it is possible to distribute the chocolates equally among Alice and Bob.Test case 33: There are total 33 chocolates. These chocolates cannot be divided equally among Alice and Bob.Test case 44: Alice and Bob cannot have equal number of chocolates, no matter how they distribute the chocolates.
Chocolate BarProblem Statement:Two friends, Alice and Bob, want to share a chocolate bar. Each square of the chocolate bar has a number on it.Alice wants to divide the chocolate bar into contiguous segments such that:The length of the segment matches Bob's birth month.The sum of the numbers on the squares within the segment equals Bob's birth day.Your task is to determine how many ways Alice can divide the chocolate bar according to Bob's birth day and month.Input Format:The first line contains an integer n, representing the number of squares in the chocolate bar.The second line contains n space-separated integers, representing the numbers on the chocolate squares.The third line contains two space-separated integers, d and m, representing Bob's birth day and birth month.Constraints:1 <= n <= 1001 <= number on chocolate square <= 51 <= d <= 311 <= m <= 12Output Format:The number of ways Alice can divide the chocolate bar satisfying Bob's birth day and month.Example:Consider a chocolate bar with numbers on the squares: [2, 2, 1, 3, 2]If Bob's birth day is 4 and his birth month is 2, Alice wants to find segments with a length of 2 and a sum equal to 4. In this case, two segments are meeting her criteria: [2, 2] and [1, 3].Sample Test CasesTest Case 1:Expected Output:52 2 1 3 2422Test Case 2:Expected Output:52 2 2 2 2430Test Case 3:Expected Output:12211
Mark is getting a piñata for his birthday party. The 4 children at the party are going to take turns trying to break it open. If each child gets one turn, in how many different orders could the children take turns?
Two friends, Taylor and Lautner, want to share a chocolate bar. Write a program that takes the chocolate bar's weight as input, calculates the equal division, and then output how much each person gets when it's equally divided.
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