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# Emma's Dilemma

Extracts from this document...

Introduction

## Emma's Dilemma                                     Kevin Etuk  28/3/02

Here are my Different arrangements for the letters in the name Emma:

Emma , emam, eamm, mmae, mmea, meam, amem, aemm,

Mema, mame, maem, amme, amem, aemm,

There are 12 different variations you can make from the letters in the name Emma.

Lucy

Here are my Different arrangements for the letters in the name Lucy:

Lucy, ucyl, cylu, ycul, luyc, ucly, cyul, yclu, lcuy, ulcy, culy, yulc, lcyu,

ulyc, cuyl, yucl,lyuc, uycl, clyu, ylcu,lycu, uylc, cluy, yluc

I have found 24 Variations you can make with the name Lucy.

If you take the one letter from Emma you can make 3 different Arrangements. If you Times 3 by 4 you get 12 which is the total number of variations.

Middle

There are only 4 variations and the rule is: 2 X 2 = T there is not much to be done with this one.

With  a 3 letter word with different letters I would get

Jim, Jmi, mij, mji, ijm, imj

And a 2 letter name with 2 letters. Would be 2 different variations.

I have figured out that….

For a 6 letter word (different letters) it would be 6 X 120 which is 720                                                                           For a 7 letter word (different letters) it would be  7 X 720 which is 5040                                     For a 8 letter word (different letters) it would be 8 X 5040 which is 40320                                                and so on…..

Table

 Number of Letters (different) Variations 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320

The only rule I can think of is N*  = V

Conclusion

160;                                                                                                          for 7 it would be 2520                                                                                                                       For 8 it would be 20160
 Number of Letters Variations 2 1 3 3 4 12 5 60 6 360 7 2520 8 20160

Each of these is half what I got for the different letter words.

The rule for this one is N *-1 = V

Following logically from my results above The for the a word with 3 of the same letters is N*-2 =V

The rule for a word with 4 letters the same is N*-3 = V

N = the number of letter in the word                                                                                                    * = the number of variations starting with the same letter                                                                V = the total number of variations

And so on.  Unless I was ment to change the rule of matermatics I think I’ve done all I can do on this topic. I kept it short and sweet without any of the Unnecessary stuff…which I you can’t see already see this last little paragraph is.

This student written piece of work is one of many that can be found in our GCSE Emma's Dilemma section.

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