Solve Stamp Denomination Problems: 1-100 with Up to 3 Stamps

  • Thread starter feynomite
  • Start date
In summary, the first problem can be solved using the coins problem with a minimum of 4 stamps, the maximum amount of distinct numbers a set of size n can produce is n^2, and the furthest a set of n stamps can reach is (n+1)n/2.
  • #1
feynomite
22
0
This is a question I recently solved, but only with brute force computation. I don't know how to represent it with mathematics and am interested if anyone could help out. I'd also be impressed if anyone came up with the solution, and even more impressed for a generalized way to solve problems of this type. Here it goes:

You have to create a set of stamps wherein you can produce all numbers from 1 to 100 from the sum of up to 3 stamps. Integers only, of course.

What's the minimum number of stamps needed? Call this number K. How many different sets of stamps of size K complete the solution? This I've computed, but don't know how to count it otherwise.

Other alterations: what's the furthest a set of n stamps can reach? Example:
n=1: [1] goes up to 3.
n=2: [1, 3] goes up to 7.
n=3: ?
Also computed, but would have no idea how to count.

And here's a permutation I'm stuck on right now.. what's the maximum amount of distinct a set of size n can produce? This is a weird combinatorics problem that I cannot grasp...
n=1: 1.
n=2: 9.
n=3: 21.
n=4: ?

Thanks all for your input, and have fun :)
 
Physics news on Phys.org
  • #2
For the first problem, you can solve it using the coins problem. The minimum number of stamps required is 4, and they would be 1, 3, 6, and 10. Any set of 4 stamps with these values would be able to produce all integers from 1 to 100.For the second problem, the maximum amount of distinct numbers that a set of size n can produce is n^2. The maximum amount of distinct numbers that a set of size 4 can produce is 16.For the third problem, the furthest a set of n stamps can reach is (n+1)n/2. For example, with n=3, the furthest the set of stamps can reach is (3+1)3/2 = 6.
 

1. How do I solve stamp denomination problems?

To solve stamp denomination problems, you need to first understand the concept of denomination. Denomination refers to the value of a stamp, which is usually indicated by a number. To solve these problems, you will need to use basic math skills and logic to determine the correct combination of stamps to make a given value.

2. What is the maximum number of stamps that can be used in these problems?

The maximum number of stamps that can be used in these problems is three. This is because the problem specifies that up to three stamps can be used to make a value between 1 and 100.

3. Can I use any combination of stamps to solve these problems?

No, you cannot use any combination of stamps to solve these problems. The stamps must be of different denominations and cannot be repeated. For example, you cannot use three 20-cent stamps to make 60 cents.

4. Are there any tips for solving these problems?

Yes, there are a few tips that can help you solve stamp denomination problems more efficiently. First, start by using the highest denomination stamp possible. Second, use a combination of stamps that leaves the least number of remaining stamps to be used. Finally, use your logic to determine the most efficient combination of stamps.

5. Are there any online resources or tools that can help with these problems?

Yes, there are many online resources and tools available to help with stamp denomination problems. You can use online calculators, step-by-step guides, and interactive games to practice and improve your skills in solving these problems.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
12
Views
912
  • Set Theory, Logic, Probability, Statistics
Replies
7
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
604
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
  • General Math
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
2K
  • Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
Back
Top