-Meam
-Aemm
-Emam
-Eamm
-Maem
-Mmae
-Mmea
-Amme
-Amem
-Mame
-Mema 12 Combinations
It has been difficult to produce a formula straight away because of the repeated letter ‘M’. I have decided to move on to a four-letter name in which all the letters differ, LUCY.
- LUCY
-Lucy
-Lcuy
-Lycu
-Lcyu
-Lyuc
-Luyc
-Ulcy
-Ulyc
-Uycl
-Uylc
-Ucly
-Ucyl
-Clyu
-Cluy
-Cyul
-Cylu
-Culy
-Cuyl
-Ylcu
-Yluc
-Yucl
-Yulc
-Ycul
-Yclu 24 Combinations
The name LUCY proves that a word with two letters the same has fewer combinations because it has 24 combinations, where as EMMA had only 12 combinations. I have decided to use a “Shriek” (also known as a ‘Factorial’), which is resembled as a ‘!’. This causes a number (e.g. 5) to be multiplied my its predecessors (e.g. 5x4x3x2x1). This number is the amount of letters in the word (N). This gives the same answer to the number of combinations as the name (e.g. a four letter word, LUCY, has four letters, so N! = 4x3x2x1 = 24, the same number of combinations in my previous example).
The words with two (or more) of the same letters has to be taken into account, so I will divide the formula N! by D! (D! is the number of different letters – Shrieked).
So therefore the formula is now N!/D!. This works for most of the words, but when they get higher, it does not works as well as it should be. I have decided that something is missing from my formula which changes a variable (such as Palindromes, which I encountered). I will have to change my formula.
- OTTO
-Otto
-Otot
-Toto
-Toot
-Ttoo
-Oott 6 Combinations
Compared to names which have two of the same letters (e.g. EMMA) which has 12 combinations, ‘Palindromes’ have fewer combinations (OTTO for example has only 6). I have decided to tackle this by dividing the whole formula by half, as palindromes have half that of normal four letters with two (or more) letters that are the same. I will notify this by an ‘M’.
So the new formula is (N!/D!)/M.
This solves all my other problems, but to make sure, I will try it out with other words.
- OTEETO (this is not a name, but just an example, the word being a proper
name does not change the outcome)
(N!/D!)/M
= (6!/3!)/2 = 240 Combinations, this is correct to the manual way, meaning my formula works.