There are some people playing a card game. On the table there are fifty cards, numbered 1 to 50, all facing up. Each player is allowed to choose a certain numbe

There are some people playing a card game. On the table there are fifty cards, numbered
1 to 50, all facing up. Each player is allowed to choose a certain number of cards. If the
sum of the numbers on all the cards chosen by the player is the highest, then he/she is
the winner. There is only one winner.
Questions:
What is the lowest possible score that makes a player a sure winner if each player has
to choose:
(a) [2 points] two cards?
(b) [2 points] three cards?
(c) [2 points] five cards?