TCS Company Logical Reasoning Mathematical Reasoning

A game is played between 2 players and one player is declared as winner. All the winners from first round are played in second round. All the winners from second round are played in third round and so on. If 8 rounds are played to declare only one player as winner, how many players are played in first round?

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TCS Other Question

36 people {a1, a2,...,a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3},....,{a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is Peter and paul are 2 friends.Sum of their ages is 35 years.Peter is twice as old as paul was when peter was as old as paul is now.What is the present age of peter?