marriage problem

 Suppose you decide to marry, and to select your life partner you will interview at most 100 candidate spouses. The interviews are arranged in random order, and you have no information about candidates you haven’t yet spoken to. After each interview you must either marry that person or forever lose the chance to do so. If you have not married after interviewing candidate 99, you must marry candidate 100. Find a strategy to maximize the probability of choosing  the best spouse. For example, a simple strategy of marrying the first candidate will ensure best spouse with  probability 1/100. 

combinatorics- coloring of points in plane

There are k colors given. Every point in a 2 D plane carries  exactly one of these k colors. what are the values of k, for which there will necessarily exist a rectangle with vertices having same color. In particular, what is maximum value of k. 

coin weighing

There are   10 piles containing large number of coins. Coins in same pile all weigh same but may differ from coins in other piles. It is given that all  coins weigh 1 gram, 2 gram or 3 gram. You have a digital weighing machine, to measure any weight. You can pick as many coins as you wish from the piles.How will you ascertain weight of all coins in minimum number of weighments.