what is the greatest int num that CANNOT be formed by adding 3,6,13 (you can use 3,6,13 as many times u want?

Question

maximum number which cannot be formed by 3,6,13 after which all number can be formed by using these three number. I need the answer also algorith about how you come to thsi result.
Example 21 can be build by adding 3 7 times. 25 can be build by 3+6+13+3. I need highest number which cannot be build by these number and above which all number cann be build by using these three number. Thanks

Answer 1

23

Any number exactly divisible by three can be represented just using the three. Any number that yields a remainder of 1 when divided by three and is at least 13 can be represented as 13 plus some number of 3s. Any number that yields a remainder of two when divided by three and is at least 26 can be represented as 13+13+some number of threes. Because all numbers must have a remainder of either 0, 1, or 2 when divided by 3, all numbers at least 26 can be represented with one of these schemes. It is easily seen that adding the ability to include more than two 13s, or any number of sixes, adds no additional power to the system. Therefore, the greatest number not representable would be the largest number less than 26 and having a remainder of 2 when divided by three. This number is 23.

Answer 2

4

Answer 3

23 but no algarithom for it

Answer 4

your question is long