Question

I am totally lost on problem set 2. i can make certain combinations. the whole idea of x+1,x+2,x+3, etc is foreign to me. what is x supposed to represent. any help is greatly appreciated!

Answer 1

It is an algebraic variable. That means that you are supposed to be able to replace it with a number to make the equation true.
What that means in the problem set is:
If you take any number add 1, to it then add 2 (to the original number not he sum of 'original number'+1), then 3, then4, then 5, if all 6 numbers are can be reached by some combination of 6, 9, and 20 then any number higher then the original number can be reached using some combination of 6, 9, and 20.

Answer 2

x is a variable which is a natural number and you have to find 6 consecutive numbers (x, x+1,x+2,x+3,x+4,x+5) such that each of these 6 numbers can be represented by some combination of 6, 9 and 20. Then according to the theorem any number >=x can be represented by the combination of 6,9, 20.All you have to do is find that very first value of x for which there are 6 consecutive values (including x) satisfying the equation 6a+9b+20c=n (where n will take value of the number that you are checking, like x)