Real World Problem (word problem)

[jdpaul127]

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]

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

 

[JeffM]

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?

 

[Deleted member 4993]

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]

There are about 230 million to list. Does excel have that range?

With some rational and severe removal.

 

[pka]

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]

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

 

[JeffM]

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]

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]

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.