Arranging Letters

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Arranging Letters

Firstly we arrange EMMA's Name.

1)EAMM 7)MAEM

2)EMAM 8)MAME

3)MEMA 9)AMME

4)MEAM 10)AEMM

5)MMEA 11)AMEM

6)MMAE 12)EMMA

.

.

Secondly we arrange Lucy's name.

1)Lucy 12)Cyul 22)Yulc

2)Luyc 13)Culy 23)Ycul

4)Lycu 14)Culy 24)Yluc

5)Lcuy 15)Cylu 25)Ucyl

6)Lcyu 16)Clyu

7)Ulcy 17)Cuyl

8)Ucly 18)Yluc

9)Uycl 19)Yucl

10)Ulyc 20)Yclu

11)Uylc 21)Ylcu

From these 2 investigation I worked out a method, To Use My Method I

Preferred To Convert Letters into Numbers, It Makes No Difference:

Step1: 1234---Do the last two number first then you get 1243.

1243---Do the last three numbers and try the possibility. 1423. 1432.

1342.1324, because the number 2 has been the first number of last

three numbers, so we don't do it again.

Step2: we have list all arrangements of 1 go front, so we do 2 go

front. 2134 and we do same thing to it, it will look like this:

2134---2143, 2143---2431,2413,2314,2341

Step3: We have finished 2 go first, then let's do 3 go ahead.

3124---3142, 3142---3241,3214,3412,3421

Step4: We have finished 3 go ahead, then try 4

4123---4132, 4132---4231,4213,4312,4321

We have list all arrangement of 1234, use this method we can arrange

the number which has 5 figures or more.

We are trying to work out a formula which can calculate the number of

arrangement when we look at a number.

Let's list all the arrangement for 1234:

1234 4123

1243 4132

1324 --- 6 arrangement 4231 ---- 6 arrangement

1342 4213

1432 4321

1423 4312

2134 3124

2143 3143

2341 ---- 6 arrangements 3241 --- 6 arrangements

2314 3214

2413 3412

2431 3421

So if we multiply 6 by 4, we would get 24, and we can get the total

arrangements of 24.

Let's try 5 figures:

12345 13245

12354 13254

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