# Real World Problem (word problem)

#### jdpaul127

##### New member
So i guess this is the best way to word this real problem.
Find all sets of 5 integers that average to 23 and fall between 1 and 47. Also can this be done in excel.

#### tkhunny

##### Moderator
Staff member
Excel is the easy part, since you can actually list all sets of 5 integers between 1 and 47.

#### JeffM

##### Elite Member
Excel is the easy part, since you can actually list all sets of 5 integers between 1 and 47.
There are about 230 million to list. Does excel have that range?

#### Subhotosh Khan

##### Super Moderator
Staff member
So i guess this is the best way to word this real problem.
Find all sets of 5 integers that average to 23 and fall between 1 and 47. Also can this be done in excel.
What would be the sum of those 5 integers?

#### tkhunny

##### Moderator
Staff member
There are about 230 million to list. Does excel have that range?
With some rational and severe removal.

#### pka

##### Elite Member
So i guess this is the best way to word this real problem.
Find all sets of 5 integers that average to 23 and fall between 1 and 47. Also can this be done in excel.
There are about 230 million to list. Does excel have that range?
If one looks at this expansion at the term $$\displaystyle 2425131x^{115}$$ we see the count is 2425131 sets of five integers $$\displaystyle 2\le n\le 46$$ that have an average of $$\displaystyle 23$$

#### Romsek

##### Full Member
Mathematica is showing 28447 length 5 partitions of 23x5=115 using the integers lying between 1 and 47 inclusive, allowing repeats.

#### JeffM

##### Elite Member
If one looks at this expansion at the term $$\displaystyle 2425131x^{115}$$ we see the count is 2425131 sets of five integers $$\displaystyle 2\le n\le 46$$ that have an average of $$\displaystyle 23$$
And you got this from excel by what method?

#### JeffM

##### Elite Member
Mathematica is showing 28447 length 5 partitions of 23x5=115 using the integers lying between 1 and 47 inclusive, allowing repeats.
And you got this from excel how!

#### pka

##### Elite Member
And you got this from excel by what method?
Actually that is the number of ways that the number 115 can be gotten using integers from 2 to 46.
I now think that is a gross overcount. That is, $$\displaystyle 24+45+46=115$$ is counted six times.
I do not know how to correct for that.
On another note. There is a style-manual for test contributors. It gives advice on generally accepted ways to word difficult phrases.
Here is an example. $$\displaystyle n$$ is an integer between $$\displaystyle 1~\&~9$$ means that $$\displaystyle n=2,~3,\cdots,~8$$ .
Now hold on, before anyone objects: what does between mean? Is $$\displaystyle 1$$ between $$\displaystyle 1~\&~9~?$$
On the other hand, saying $$\displaystyle n$$ is an integer from $$\displaystyle 1\text{ to } 9$$ makes inclusion very clear.