Puzzle question:?

Question

Could someone please help me cracking the puzzle?

In a shop, a burger can be purchased in quantities: 6, 9 and 20 only. Looking at this, we can say one can purchase exactly 15 pieces by buying a 6 and a 9, but can’t buy exactly 10 burgers. What is the maximum number of burgers that a customer cannot purchase?

Answer 1

I would say that there is no set number, because as you go up, there will constantly be numbers that arent divisibly by 6, 9 and 20.  

There are easy ways to tell if a number is divisible by a certain number.  

For 6, if you add up all of the digits numbers, and they equal 3, 6, or 9, and the number is even, it is divisible by 6.(ex. 7896 7+8+9+6=30 which is 3+0 which is 3, and its even, so yes)

for 9, you add up all of the digits of the numbers, and if it equals 9 it is divisible by 9.

For 20, you only need to pay attention to the last 2 digits.  If the last 2 digits are 20, 40, 60, 80 or 00  then the number is divisible by 20.

So, based on this, even an arbitrarily large number will not be divisible by neither 6, 9, nor 20.  an example of such large number would be 98712632782391.