Emmas dilemma

Authors Avatar

Investigation

I am first going to write out all the combinations for the name Emma.

emma

eamm

emam

meam

maem

mmea

mmae

mema

mame

amme

aemm

amem

This proves that if a name has the same arrangements of letters they will have the same total number of different combinations. However, this does not give me sufficient information to develop a formula. I am now going to look at names with 2 letters the same like Emma, but with a different total number of letters.

I am going to look at all the combinations for the name Lucy.


Lucy has 24 different combinations. This means that all names with 4 different letters will have a total of 24 different combinations. I am now going to look at different names with different numbers of letters. All the names I investigate will all have different letters.

Join now!

Name: Jo

Total number of letters: 2

jo

oj

Jo has 2 different combinations.

Name: Ian

Total number of letters: 3

ian

ina

ani

ain

nai

ain

Ian has 6 different combinations. I have realised that the total number of combinations is the number of letters multiplied by the previous number of combinations.

Name: Lucy

Total number of letters: 4

Previous number of combinations: 6

Prediction: 4 x 6 = 24

lucy

luyc

lcyu

lcuy

lycu

lyuc

ulcy

ulyc

uylc

uycl

ucly

ucyl

cluy

clyu

culy

cuyl

cyul

cylu

yluc

ylcu

yclu

ycul

yucl

yulc

As i predicted 24 combinations. ...

This is a preview of the whole essay