To investigate the various arrangements that could be made with different names or words. In doing so, I hope to find a pattern and figure out a formula to make this more simple.

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Maths Coursework : Emma’s Dilemma

Thursday 5th December 2002

Lena Tran

Aim: To investigate the various arrangements that could be made with different names or words. In doing so, I hope to find a pattern and figure out a formula to make this more simple.

Investigation One:

First Arrangement:

I am going to investigate how many words can be created using the name “EMMA” :

 

I have created 12 words out from EMMA. Seeing as EMMA has two M’s in it, the outcome of different arrangements were not much, as the two M’s stop the letters from being arranged, so that the words cannot repeat.

To do this, I used the previous word I wrote and rearranged 2 of the letters.

E.g. M E M A, changing the E and A around, I have created M A M E.

Second Arrangement

This time, I will be investigating how many words can be created using the name “LUCY”. LUCY has all different letters in it, so it will be different from EMMA.

I have created 24 words out from LUCY. This is much more than the number of arrangements made from the name, EMMA. This is because even though they have the same amount of letters, EMMA has fewer arrangements due to the two M’s in her name.

To do this, I used a different method. I took one of the letters and kept it in the start of the word, and then rearranging the other three.

E.g. LUCY can change into LCYU.

Then, from this new arrangement, I changed the last two letters, in order to make another arrangement.

E.g. from LCYU into LCUY

Investigation Two:

I am now going to choose different names and rearrange the letters to make different words. I will start with an investigation of a word with two letters, then three and then four.

First Arrangement:

I will be investigating the name “JO”.

As there was only two letters in this name, all I needed to do was switch the first letter with the second letter.

E.g. JO changes to OJ.

Second Arrangement:

I will be investigating the name “KAT

Using the same technique used to find the words for LUCY, I have kept the first letter at the start and rearranged the other two. From this method, I have found 6 ways of rearranging the name “KAT”.

Join now!

Third Arrangement:

I will be investigating the name “RITA

I have created 24 different arrangements using the name RITA. This is the same amount of arrangements found when rearranging LUCY’s name. This is because they are quite similar, as they both have four letters and each letter is different from each other. I will now draw a table showing my results:

Looking at the table above, I have realised a pattern between the letters and arrangements. If I multiply the number of letters by the number of arrangements made from the previous pattern, I will ...

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