a) Determine which amounts of postage can be formed using just 4 cent stamps and 11 cent stamps. b) Prove your answers to a using strong induction.
(I am only working on part a for now)
I saw that this problem was a variation of this one 12 or more cents but that one came with the initial bounds, "Prove that every amount of postage of 12 cents or more", but here, you have to come with the initial bounds. I watched a Youtube video on how to do that problem Youtube: Strong Induction and here's the author's basis case
Here's my work off that author's basis case
12 = 3(4) + 0(11)
19 = 2(4) + 1(11)
26 = 1(4) + 2(11)
33 = 0(4) + 3(11)
And my conclusion is that postage of 12 + multiples of 7 can be formed with just using 4 cent stamps and 11 cent stamps. Is that the correct conclusion to which amounts of postage can be formed using just 4 cent and 11 cent stamps? I wasn't completely sure because 4 can be formed with just using 1 cent stamp but I felt like there was a reason you start from 12 in the other problem, to make the induction step easier? Would you have to include numbers like 4 and 11?