Firstly we arrange EMMA's Name.
)EAMM 7)MAEM
2)EMAM 8)MAME
3)MEMA 9)AMME
4)MEAM 10)AEMM
5)MMEA 11)AMEM
6)MMAE 12)EMMA
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Secondly we arrange Lucy's name.
)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:
234 4123
243 4132
324 --- 6 arrangement 4231 ---- 6 arrangement
342 4213
432 4321
423 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:
2345 13245
2354 13254
2435 --- 6 arrangements 13452 --- 6 arrangements
2453 13425
2534 13524
2543 13542
4235 15432
4253 15423
4352 --- 6 arrangements 15324 ---- 6 arrangements
4523 15342
4532 15243
4325 15234
Don't you notice the arrangements of last 4 numbers added up, it equal 24, so if we times 24 by 5, and get 120, and 120 is the total of arrangements.
if a number has 6 figures, then the total of arrangement should be 120 times by 6, and get 720, and 720 is the total of arrangements.
)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.
)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:
234 4123
243 4132
324 --- 6 arrangement 4231 ---- 6 arrangement
342 4213
432 4321
423 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:
2345 13245
2354 13254
2435 --- 6 arrangements 13452 --- 6 arrangements
2453 13425
2534 13524
2543 13542
4235 15432
4253 15423
4352 --- 6 arrangements 15324 ---- 6 arrangements
4523 15342
4532 15243
4325 15234
Don't you notice the arrangements of last 4 numbers added up, it equal 24, so if we times 24 by 5, and get 120, and 120 is the total of arrangements.
if a number has 6 figures, then the total of arrangement should be 120 times by 6, and get 720, and 720 is the total of arrangements.
