This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".

Alice is a kindergarten teacher. She wants to give some candies to the children in her class.  All the children sit in a line and each of them has a rating score according to his or her performance in the class.  Alice wants to give at least 1 candy to each child. If two children sit next to each other, then the one with the higher rating must get more candies. Alice wants to minimize the total number of candies she must buy. Example arr =  [ 4, 6, 4, 5 , 6 , 2 ] She gives the students candy in the following minimal amounts: [ 1, 2, 1, 2,  3, 1 ] . She must buy a minimum of 10 candies. Function Description Complete the candies function in the editor below. candies has the following parameter(s): int n: the number of children in the classint arr[n]: the ratings of each studentReturns int: the minimum number of candies Alice must buyInput Format The first line contains an integer, n , the size of arr.Each of the next n lines contains an integer arr[ i ] indicating the rating of the…

Alex is playing Poker card game. He starts with a deck of N cards, where for each valid (i), the ith card has an integer A¡ written on it. Now the dealer starts dealing the cards one by one in the order from card 1 to card N. Alex wins if at some moment in time, the sum of all the cards dealt so far is between X and Y inclusive; if this never happens, Alex loses. You are now helping Alex to win the game, so without him noticing, you will swap some pairs of cards before the game starts. Develop a python script to find the smallest number of swaps we need so that Alex would win the game, or find that it is impossible to make Alex win. Display a single line containing one integer i.e., the smallest required number of swaps or -l if Alex cannot win. Input: 5 15 22 10 15 22 4 19 Output: 1

Consider a game in which two players take turns removing any positive number of matches they want from one of two piles of matches. The player who removes the last match wins the game. Show that if the two piles contain the same number of matches initially, the second player can always guarantee a win.

There are four people who want to cross a rickety bridge; they all begin on the same side. You have 17 minutes to get them all across to the other side. It is night, and they have one flashlight. A maximum of two people can cross the bridge at one time. Any party that crosses, either one or two people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown, for example. Person 1 takes 1 minute to cross the bridge, person 2 takes 2 minutes, person 3 takes 5 minutes, and person 4 takes 10 minutes. A pair must walk together at the rate of the slower person's pace. Write the specification of an algorithm that solves the problem.