Ramesh and Suresh decided to play a game of numbers. In this game, each person calls out a number which is less than or equal to n, alternatively. The rules of the game are as follows: 1. Ramesh starts the game by calling out the first number and he always calls out an odd number. 2. Suresh will always call out an even number. 3. Each of them will call out a number greater than the previous number. (Ramesh can choose any odd number at the start of the game.) 4. The game ends when the players cannot call the next number. For example, if n = 6, then following represents the possible games; {1, 6}, {5, 6}, {3, 4, 5, 6}, {1, 2, 3, 4, 5, 6} etc. The length of any game is defined as the total number of numbers which were called out. i.e. length of the game {1, 6} is 2 and the length of the game {3, 4, 5, 6} is 4 Find the number of different possible games of length k played by Ramesh and Suresh. Provide detailed solution and win Rewards Points. |
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