1. ## Postage Stamps Problem?

You have an unlimited supply of 5 cent stamps and 11 cent stamps. What is the greatest amount of postage you cannot make by using the stamps?
1.When will it work?(What numbers)
2.What's the pattern?
3.Why does it work?

I know it's 39 cents but I don't really know the pattern and steps to get there?

2. ## Re: Postage Stamps Problem?

Originally Posted by kikhakplz
You have an unlimited supply of 5 cent stamps and 11 cent stamps. What is the greatest amount of postage you cannot make by using the stamps?
1.When will it work?(What numbers)
2.What's the pattern?
3.Why does it work?
I know it's 39 cents but I don't really know the pattern and steps to get there?
I will not simply give answers. I think that to do is to learn.
Basically you want to look at $5m+11n$ where $m~\&~n$ are non-negative integers.
So list the sums less than $40$. Here is a start: $5,~10,~11,~15,~16\cdots$ Show each is made-up.
Then show how $40\text{ to }50$ can each be made.
When you do that work, then you are ready to ask why.

3. ## Re: Postage Stamps Problem?

40 = 8 x 5
41 = 1 x 11 + 6 x 5
42 = 2 x 11 + 4 x 5
43 = 3 x 11 + 2 x 5
44 = 4 x 11 + 0 x 5
45 = 9 x 5
46 = 41 as above + 5
47 = 42 as bove + 5
and so on

Does that count as the pattern?

4. ## Re: Postage Stamps Problem?

So all numbers above 39 can be represented by 5x + 11y correct?

5. ## Re: Postage Stamps Problem?

Originally Posted by kikhakplz
So all numbers above 39 can be represented by 5x + 11y correct?
Why is that the case? Show us, $73=5m+11n$ What are $m~\&~n~?$

6. ## Re: Postage Stamps Problem?

Originally Posted by Plato
Why is that the case? Show us, $73=5m+11n$ What are $m~\&~n~?$
So I subtracted 73 by 33 to make the number divisible by 5, and I get 5->(73-33)/5=8 11->(73-5x8)/11=3

7. ## Re: Postage Stamps Problem?

Originally Posted by Plato
Why is that the case? Show us, $73=5m+11n$ What are $m~\&~n~?$
I realized that I just need to make the number greater than 44 be divisible by 5 then I will be able to find out.
That number can be subtracted by 11, 22, 33 ,44 ,0 right?

How do I put this into the pattern?

8. ## Re: Postage Stamps Problem?

Originally Posted by Plato
I will not simply give answers. I think that to do is to learn.
Basically you want to look at $5m+11n$ where $m~\&~n$ are non-negative integers.
So list the sums less than $40$. Here is a start: $5,~10,~11,~15,~16\cdots$ Show each is made-up.
Then show how $40\text{ to }50$ can each be made.
When you do that work, then you are ready to ask why.

I see, so for part one it works with 5x + 11y

9. ## Re: Postage Stamps Problem?

Originally Posted by kikhakplz
I realized that I just need to make the number greater than 44 be divisible by 5 then I will be able to find out. That number can be subtracted by 11, 22, 33 ,44 ,0 right? How do I put this into the pattern?
Take $98\\87\\76\\65$
There we have it. We have a multiple of five, $65$.
So $98=3(11)+13(5)$

10. ## Re: Postage Stamps Problem?

Originally Posted by Plato
Take $98\\87\\76\\65$
There we have it. We have a multiple of five, $65$.
So $98=3(11)+13(5)$
for 87 (87-22)/5=13=#of 5

# of 11=(87-13x5/)11=2

11. ## Re: Postage Stamps Problem?

Originally Posted by kikhakplz
for 87 (87-22)/5=13=#of 5

# of 11=(87-13x5/)11=2
Look, I do not know how you think. I hope that you do not expect a quick way to get it.
I think about a programmer: Say the number is K.
Now count the number of subtractions of $11$ from the K until you have a multiple of five.
Now say that the count is $j$ That is $K-(11)\cdot j =5\cdot n$

Then put it together: $K= 5\cdot n + 11\cdot j$

Solved

Solved

Solved

15. ## Re: Postage Stamps Problem?

Solved

Page 1 of 2 12 Last