Melody

New Info (with Bertie's and Rom's help- thanks guys.)

4 letters are chosen from the alphabet.  And these are the number of possibilities.

Letters all different = 26*25*24*23=358800

letters 2 the same and other 2 different= 26*1*25*24*4C2= 93600

letters 2 pairs =  26*1*25*1*4C2 divided by a half (got it) = 1950    

I had to halve it because for each pair left there are 2 that are the same.

letters 3 the same=26*1*1*25*4C3=2600

Letters all the same=26

Now I know it should add up to 26⁴=456976 and they do so that is great!

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I might use this to figure out something else later.  Mmm not sure!

Thank you.

What about my detailed answer?  

Thanks for the points Quazars - We all like those. 

Zegroes, the problem with your logic is that you are taking 20% off the original amount each year.

NOT 20% of the the NEW amount.

sorry - I was called a way on a phone call. 

$$\begin{array}{rlll}
100000\times 0.8^n &<&1000&\\\\
100000\times 0.8^n &<&1000&\mbox{ Divide both sides by 100000}\\\\
0.8^n &<&0.01&\mbox{ When you are looking for a power you must take the log (a log IS a power)}\\\\
log0.8^n &<&log0.01&\mbox{ }\\\\
nlog0.8&<&-2&\mbox{Remember: log 0.8 is negative }\\\\
n&>&\frac{-2}{log0.8}&\mbox{ }\\\\
n&>&20.63&\mbox{ }\\\\


\end{array}$$

So it will take 21 wars.

okay.  We hardly ever give minus points here.  Zegroes was just trying to help.

So give Zegroes back his points and then I will help you.  

pi is an irrational number which means that it cannot be be expressed exactly as a decimal or as a fraction. (not even a recurring fraction)

So any number representation of pi will be an approximation.

Okay, I get you. Thanks Bertie.

This tell me my missing category that is certainly true but the permutations are still causing problems.

I think that I have it all sorted now.

4 letters are chosen from the alphabet.  And these are supposed to be the number of possibilities  but something is wrong!

Letters all different = 26*25*24*23=358800

letters 2 the same and other 2 different= 26*1*25*24*4C2= 93600

letters 2 pairs =  26*1*25*1*4C2 divided by a half (got it) = 1950    

I had to halve it because for each pair left there are 2 that are the same.

letters 3 the same=26*1*1*25*4C3=2600

Letters all the same=26

Now I know it should add up to 26⁴=456976 and they do so that is great!

$$\\z=3k+i+\frac{1}{10}*(12+k)+(3k-4)i\\\\
z=3k+i+\frac{12+k}{10}+(3k-4)i\\\\
z=\frac{30k}{10}+\frac{12+k}{10}+(3k-4)i+i\\\\
z=\frac{12+31k}{10}+(3k-3)i\\\\$$