Rohan is a huge soccer fan so he wants to catch a game of the UEFA Champions League (UCL) while he is in Europe. Assume UCL has k participating teams, where k is a positive even integer. Suppose that the organizer of the league decides that there will be a total of k2 matches this season, where no pair of teams plays more than once against each other (ie. if Paris and Barcelona play a match against each other, they never play against each another again for the rest of the season). Prove that if every team has to play at least one match this season, then there is no team that plays two or more games.

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

There is an upcoming football tournament, and the n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of  matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all  matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English.Please give time complexity. list of results mean Any combination of wins, losses and draws. You may wish to view this as a mapping from the set of…