My predictions was correct this time.
MIKE: I predict there will be 24 combinations because all 4 letters aredifferent
M I K E M I E K M K I E M K E I M E K I M E I K K I M E K I E M K E M I K E I M K M I E K M E I I M K E I M E K I E K M I E M K I K E M I K M E E I M K E I K M E K I M E K M I E M I K E M K I
My prediction was Correct again.
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Thought: I Want to know what would happen if I chose a name like Anna, because there are 2 different letters which are paired with the same letter. So I will predict there will be 6 combinations because so far the number of combinations was halved each time 1 letter turned into a pair.
ANNA:
A N N A A N A N A A N N N A A N N A N A N N A A
My prediction was correct so this means that so far I found out that:
4 letters different = 24 combinations
3 letters different = 12 combinations
2 letters different = 6 combinations
I will now try the letter ozzz because that also has 2 different letters but 3 are the same and 1 is different. I predict there will be less than 6 so lets say 3 combinations.
OZZZ:
O Z Z Z Z O Z Z Z Z O Z Z Z Z O
My predictions was wrong because there are more than 3 combinations there are 4. This would mean that my initial theory is wrong. Here is the table again with the added information.
4 letters different = 24 combinations
3 letters different = 12 combinations
2 letters different (2&2) = 6 combinations
2 letters different (1&3) = 4 combinations
I cannot see an obvious connection with the letters at the moment so I will try 5 letters in a word to see if I can find a pattern from there.
JAMES: I predict there will be 100 combinations to the name James.
J A M E S J A M S E J A S M E J A S E M J A E S M J A E M S J M A E S J M A S E J M S E A J M S A E J M E S A J M E A S J E S A M J E S M A J E M A S J E M S A J E A M S J E A S M J S A E M J S A M E J S M A E J S M E A J S E A M J S E M A
So far there are 24 combinations and I have only done one letter at the beginning, so I have a theory that if you substitute the J for any other letter that will give you another 24 combinations, so that’s would mean there are
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5 x 24 combinations = 120. If this theory is right then that would mean 4 letters would be 4 x the number of combinations of a 3 letter word. And then for 3 it would be 3 x the number of combinations of a 2 letter word, and then again the same for 2, 2 x the number of combinations of 1 letter. Which would mean 5 is, 5 x 4 x 3 x 2 x 1 = 120. And 4 x 3 x 2 x 1 = 24.
Using this theory I could predict the number of combinations of a 6 letter word where all the letters are different. So:
6 x 5 x 4 x 3 x 2 x 1 = 720
So if this is the way to work out the number of combinations when the letters are all different I now need to find out how to work out the combinations if letters are the same.
I have information for 4 letter words but I need some for 5 letter words. So I will try the name Sarah, because it had 2 letters the same and the rest different.
SARAH: I predict there will be 60 combinations because like the 4 letter words the combinations were halved when a letter was changed to the same as another.
S A R A H S A R H A S A A R H S A A H R S A H R A S A H A R S R A A H S R A H A S R H A A S H R A A S H A R A S H A A R A A R S H A A R H S A A S H R A A S R H A A H S R A A H R S A R A S H A R A H S A R S A H A R S H A A R H A S A R H S A A S A R H A S A H R A S R A H A S R H A A S H A R A S H R A A H A S R A H A R S A H S A R A H S R A A H R S A A H R A S R A A S H R A A H S R A S A H R A S H A R A H A S R A H S A R S A A H R S A H A R S H A A R H A A S R H A S A R H S A A H A R A S H A R S A H A S A R H A S R A H A A R S H A A S R H S A A R H S A R A H S R A A H R S A A H R A S A H R A A S
My prediction was correct which would show that 120 / 2 = 60. If I tried the name Billi I predict I would get a total of 30 combinations because there are 2 pairs of the letters the same. Which would be 120 / 2 / 2.
BILLI:
B I L L I B I L I L B I I L L B L I I L B L I L I B L L I I
I I L L B I I L B L I I B L L I B L L I I B L I L I B I L L
I L L I B I L L B I I L I L B I L I B L I L B I L I L B L I
L L I I B L L I B I L L B I I L B I I L L B I L I L B L I I
L I I L B L I I B L L I L I B L I L B I L I B L I L I B I L
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My prediction was correct. So if I tried the combination ozzzo there would b less then 30 combinations. I predict there will be I predict there will be 20 combinations because 120 / 3 / 2 = 20.
OZZZO:
O Z Z Z O O Z Z O Z O Z O Z Z O O Z Z Z Z Z Z O O Z Z O Z O Z O Z Z O Z O O Z Z Z Z O O Z Z O Z O Z
My prediction was wrong. The number of combinations is 10, which would mean that you needed to divide 20 by 2 again. So it would be the calculation: 120 / 3 / 2 / 2. I though that you had to divide by the number of letters there are the same for each one, for example.
JAMES is 120 / 1 / 1 / 1 / 1 / 1.
SARAH is 120 / 2 / 1 / 1 / 1.
BILLI is 120 / 2 / 2 / 1.
But….
OZZZO is 120 / 3 / 2 / 2. Instead of 120 / 3 / 2.
If I tried OZZZY it might add another piece to the puzzle.
OZZZY:
O Z Z Z Y O Z Z Y Z O Z Y Z Z O Y Z Z Z Z Z Z Y O Z Z Z O Y
Z Z O Z Y Z Z O Y Z Z Z Y Z O Z Z Y O Z Z O Z Z Y Z O Z Y Z Z O Y Z Z Z Y Z Z O Z Y Z O Z Z Y O Z Z Y Z Z Z O Y Z Z O Z Y Z O Z Z Y O Z Z Z
There are 20 combinations which is 120 / 3 / 2 / 1 / 1.
So
JAMES is 120 / 1 / 1 / 1 / 1 / 1.
SARAH is 120 / 2 / 1 / 1 / 1.
BILLI is 120 / 2 / 2 / 1.
But…..
OZZZY is 120 / 3 / 2 / 1 / 1 .
OZZZO is 120 / 3 / 2 / 2.
Using this table I saw that when there is 3 letters you divide by 3 then 2, so maybe you actually divide by 1 as well but it makes no difference to the answer. So this would change the table slightly to
JAMES is 120 / 1 / 1 / 1 / 1 / 1.
SARAH is 120 / {2 / 1} / 1 / 1 / 1.
BILLI is 120 / {2 / 1} / {2 / 1} /1.
OZZZY is 120 / {3 / 2 / 1} / 1 / 1 .
OZZZO is 120 / {3 / 2 / 1} / {2 / 1}.
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Using this whole theory you can work out any number of letters with any combination of the same letter, I will draw 2 charts to show this for 10 letters and 7 letters. To show 10x9x8x7x6x5x4x3x2x1 I will write 10! As shorthand. And the same for equations like 3/2/1 or 5/4/3/2/1.
