Emma’s Dilemma.

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EMMA's Dilemma

We are investigating the number of different arrangements of 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)Ulcy 22)Yulc

2)Luyc 13)Ulyc 23)Yucl

4)Lycu 14)Culy 24)Yluc

5)Lyuc 15)Cuyl 25)Yluc

6)Lcuy 16)Clyu

7)Lcyu 17)Cluy

8)Ucly 18)Cylu

9)Ucyl 19)Cyul

10)Uycl 20)Yclu

11)Uylc 21)Ycul

From these 2 investigation I worked out a method:

Step1: 1234---Do the last two numbers 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 listed all the arrangements of 1 go front, so we do 2 go front. 2134 and

We do same thing to it, it will be 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