Emma is playing with the different arrangements of the letters in her name, here is a list of all the different arrangements:
- emma
2- emam
3- eamm
4- amme
5- amem
6- aemm
7- mmae
8- mmea
9- mema
0- mame
1- maem
2- meam
To make sure that she listed all of the possible arrangements, Emma used a systematic formula.
Lets try it with the letters abcd:
-abcd
first start off by keeping the first two letters the same and then swapping the last two letters.
2-abdc
Then keep the first letter where it is and swap all the second number with the third.
3-acbd
Now you can swap the last two numbers and keep the first two where they are.
4-acdb
Next swap the second letter with the only letter that has not been second yet which should be D, then you can swap the last two letters again.
5-adbc
6-abdc
Now that you have listed all of the arrangements for the letter A you can repeat this process but each time swap the first letter for one of the others.
7-bacd
8-badc
9-bcad
0-bcda
1-bdac
2-bdca
3-cabd
4-cadb
5-cbad
6-cbda
7-cdab
8-cdba
9-dabc
20-dacb
21-dbac
22-dbca
23-dcab
24-dcba
Emma then tried to find the different arrangements of her friend Lucy's name, she used the same systamatic formula.
- lucy
2- luyc
3- lcuy
4- lcyu
5- lycu
6- lyuc
7- ulcy
8- ulyc
9- ucyl
0- ucly
1- uycl
2- uylc
3- culy
4- cuyl
5- clyu
6- cluy
7- cyul
8- cylu
9- yclu
20- ycul
21- yluc
22- ylcu
23- yucl
24- yulc
Here are the 24 different arrangements for Lucy's name, but while she was looking over the different arrangements she noticed something strange. Even though her name and Lucy's name had the same amount of letters, Lucy's name had twice as many arrangements. Lucy thought for a moment and then realised that her name had two m's where as Lucy's name had no double letters. Lucy decided to try and find out why this was. She decided to list the different arrangements of various names with double or more letters.
- emma
2- emam
3- eamm
4- amme
5- amem
6- aemm
7- mmae
8- mmea
9- mema
0- mame
1- maem
2- meam
To make sure that she listed all of the possible arrangements, Emma used a systematic formula.
Lets try it with the letters abcd:
-abcd
first start off by keeping the first two letters the same and then swapping the last two letters.
2-abdc
Then keep the first letter where it is and swap all the second number with the third.
3-acbd
Now you can swap the last two numbers and keep the first two where they are.
4-acdb
Next swap the second letter with the only letter that has not been second yet which should be D, then you can swap the last two letters again.
5-adbc
6-abdc
Now that you have listed all of the arrangements for the letter A you can repeat this process but each time swap the first letter for one of the others.
7-bacd
8-badc
9-bcad
0-bcda
1-bdac
2-bdca
3-cabd
4-cadb
5-cbad
6-cbda
7-cdab
8-cdba
9-dabc
20-dacb
21-dbac
22-dbca
23-dcab
24-dcba
Emma then tried to find the different arrangements of her friend Lucy's name, she used the same systamatic formula.
- lucy
2- luyc
3- lcuy
4- lcyu
5- lycu
6- lyuc
7- ulcy
8- ulyc
9- ucyl
0- ucly
1- uycl
2- uylc
3- culy
4- cuyl
5- clyu
6- cluy
7- cyul
8- cylu
9- yclu
20- ycul
21- yluc
22- ylcu
23- yucl
24- yulc
Here are the 24 different arrangements for Lucy's name, but while she was looking over the different arrangements she noticed something strange. Even though her name and Lucy's name had the same amount of letters, Lucy's name had twice as many arrangements. Lucy thought for a moment and then realised that her name had two m's where as Lucy's name had no double letters. Lucy decided to try and find out why this was. She decided to list the different arrangements of various names with double or more letters.
