Only need help with b,d and f

Give a proof for each statement. (a) If a group of 9 kids have won a total of 100 trophies, then at least one of the 9 kids has won at least 12 trophies. If a person buys at least 400 cups of coffee in a year, then there is at least one day in which the person has bought at least two cups of coffee. (c) The average of three real numbers is greater than or equal to at least one of the numbers. V2 is irrational If n is an integer and n3 is even, then n is even. There is no smallest integer. (d) You can use the following fact in your proot (e) (f) There is no largest rational negative number