Question

How many skittles are in a container?
Each skittle is numbered, and we have 5 of those numbers.
1. 2105
2. 2092
3. 1093
4. 1163
5. 595
Using those 5 numbers, how can we find a formula to tell us how many skittles are possibly in the container?

Answer 1

@mathmale
@e.mccormick
Do you think you could help with this? :)

Answer 2

@Luigi0210

Answer 3

Jeff: I don't quite get this problem. What's the context in which you found it?

Answer 4

It's an AP Statistics assignment.
Basically, the professor would like to know how many skittles are in the container. Each skittle has a number, and those are the five numbers that he gave us. We are looking for a formula to determine how many could be in the container. It must a number greater than, or equal to 2,105.

Answer 5

@amistre64

Answer 6

@myininaya

Answer 7

Looks as though you may have to make some assumptions.
Question 1: Are all the skittles numbered consecutively (1, 2, 3, 4, 5, ... )? or could some numbers be omitted?

Question 2: Does the numbering system being with 1?

Answer 8

Question 1: All of the skittles are numbered.
Question 2: This is an assumption-based answer, therefore, that was all of the given data.

Answer 9

If you assume that every skittle is numbered, that the first skittle is numbered 1, the second numbered 2, and so on, and that no index (number) is skipped, then you could safely say that the total number of skittles in the container is equal to or greater than the largest of the given numbers.

If your assumptions change, your answer may change with it.

Answer 10

How would we be able to compose a formula in order to know how many skittles are in the container?

Answer 11

I don't know. I could ask you to do some experimentation and see where that gets you.

Supposing that the five numbers were 7, 17, 22, 40 and 51, could you write a formula for the maximum number of skittles in the container? Again, you must state your assumptions, e. g., that the numbering system begins with counter value n = 1 and that not necessarily every counter between 1 and the highest number (51) is used.

Think about this and propose a first solution. I very much doubt you can tell exactly how many skittles are in the container because the assumptions could vary.

Answer 12

As of right now, we know that there could be more, or less than 2,105 skittles in the container. We need to compose a formula that "could" possibly give us more, or less than 2,105 skittles. I believe he mentioned the equation should always give us more than our highest number of skittles in the container.

Answer 13

You mean "more than the largest index (counter) found among the indices used."

I chose five smaller integers to serve as an example. Supposing that we drew five skittles from the container and wrote down the indices of those skittles, we'd have { 7, 17, 22, 40 and 51}.

I'd suggest you set up various scenarios and use what you learn from them to attempt setting up the required equation.
\
Scenario 1: The smallest index is 7, not 1, not 2, not 3, .... , not 6. The number of indices actually used could be less than the number of digits between 7 and 17 (or between 17 and 22, and so on).

Take a look at that. What can you deduce?

Answer 14

In my situation, we have:
{595, 1093, 1163, 2092, 2105}
The smallest given index is 595. (This is what we know.)
I am not quite positive as to what I could deduce from the scenarios.
I am looking to compose a formula, but I have no idea as to how I could begin to compose it with the given data.

Answer 15

This hint may or may not be useful: the formula for calculating the nth term of an arithmetic sequence is l=a +(n-1)d

Jeff, I understand that. I told you the truth up front, namely, that I did not "get" an appropriate method of solution right away. So I proposed a model using smaller indices with which you and I could experiment. If you don't want to use that model, that's OK, but that puts us back to Square One. I'm disappointed that you're apparently dismissing my attempts to be helpful and without contributing anything, appear to be dumping the problem back into my lap.

Answer 16

l = 1 + (n - 1)d

I apologize...
This is a new equation for me.
How would I be able to test this formula against my given set of data?

Answer 17

Two of the indices are 1093 and 1163. What is the max number of indices that could occur here, including both the starting value (1093) and the ending value (1163)?
Hint: let l (the last index) be 1163 and a (the initial value of the index) be 1093. d is the 'jump' from one index to the very next one. What is the total number of indices we have here?

Answer 18

Between 1098, and 1163, I believe we would have 70 indices, correct?

Answer 19

That sounds high, but that may be because you typed 1098 instead of 1093.
Here l=1163, a=1093, d =1, and we are to find n.
Care to try again?
You'll have to decide for yourself whether this approach will help you or not. I'm afraid I have no other options to offer you at the moment.

Answer 20

I will be back in a few minutes. I'm on a school computer.

Answer 21

Note: if l = a + (n-1)d, then l - a = (n - 1)d, and d=1, l - 1 = n - 1.

Answer 22

So, how many indices have you, between and including the endpoints 1063 and 1163? It's not 70.

Jeff, despite the vocabulary used in stating this problem, I don't think you're going to be able to come up with an EQUATION for the number of skittles in the container. Instead, you'll probably have to settle for one or more inequalities to show the smallest and the largest possible number of skittles in the container.

Even then, there is ambiguity, because we don't know whether the container is full or just partially full. If it's a big container, we might have another 1000 skittles beyond the 2105th one.

I need to get off OpenStudy myself.

Have you a classmate with whom you could discuss this problem? If so, it might be more profitable to you to seek out one or more classmates and to pool your ideas for the solution of this problem.

Answer 23

Before you leave, I just have a brief question. How would I be able to connect your formula with my data set? Thank you.