1. ## unique combination problem

here's a problem I'm trying to help my 7th grade daughter with and I
just cant remember how to solve it...
"You are given 5 different weights, marked 1lb, 2lb, 5lb, 6lb, and
10lb. How many different weights can you obtain using these weights?"

My first thought was to do something with 5!, but that doesn't address
the need to get unique combinations.

I've tried searching in a number of different ways to find similar
problems, but can't find anything. Seems like it should be a simple

Can anyone help?

2. Originally Posted by lunaclaire
"You are given 5 different weights, marked 1lb, 2lb, 5lb, 6lb, and
10lb. How many different weights can you obtain using these weights?"
Is it clear to you the the least weight is 1lb?
The maximum is 24?
Can you get 3?
Can you get 4?
Can you get 8?
Can you get 10?
Just make a list.

3. thanks for that thought, but I'm hoping for something more than brute force and she needs to show a technique or logical approach to solving these problems in a general way

4. Originally Posted by lunaclaire
thanks for that thought, but I'm hoping for something more than brute force and she needs to show a technique or logical approach to solving these problems in a general way
Well you did say 7th grade did you not?
I think that brute force is use here to teach logical thinking.
This method is above grade level.
Expand $\left( {1 + x} \right)\left( {1 + x^2 } \right)\left( {1 + x^5 } \right)\left( {1 + x^6 } \right)\left( {1 + x^{10} } \right)$.
Then count the number of terms containing x.

5. yeah, you may be right that brute force is the only way at her level... I think my initial "do you know about factorials yet?" reply to her led me to think that there was something formulaic she may have been exposed to that would lead to an answer.

That said, can you explain a bit about that formula you last replied with and how it relates to this kind of problem?

Thanks again.