LUCY UYCL YCLU
LCUY UYLC YULC
LCYU CULY YLCU
LYCU CUYL YLUC
LYUC CLYU
LUYC CLUY
ULCY CYLU
UCLY CYUL
UCYL YUCL
ULYC YCUL
From this second experiment I have found out that when the letter “L” is at the front of the name Lucy then there are six different combinations. The same rule applies to the letters “U”, “C” and “Y” in the name Lucy.
Overall there are 24 different combinations for the name Lucy
From the first two experiments I have noticed that the name Emma has half the number of combinations when compared with the name Lucy. This maybe because of the repeated letter “M” in the name Emma. To find out whether or not this is true I will investigate a 5-letter word with a repeated letter in it and a 5-letter word with all different letters in it. I will then compare my results for these experiments.
For the third pat of my Investigation I will look at other names of varying lengths and letters. The first name I will investigate will be Penny.
PENYN PYNNE ENPNY NYPNE NEPNY YPNNE
PEYNN EPNNY ENYNP NYEPN NEPYN YENNP
PNNEY EPNYN NNEYP NYENP NEYPN YENPN
PNNYE EPYNN NNEPY NPYNE NEYNP YEPNN
PNENY EYNNP NNPYE NPYEN YNNEP YPENN
PNYNE EYNPN NNPEY NPEYN YNNPE PENNY
PNYEN EYPNN NNYEP NPENY YNPEN YPNEN
PNEYN ENNPY NNYPE NPNEY YNPNE ENPYN
PYENN ENNYP NYNPE NPNYE YNENP NYPEN
PYNEN ENYPN NYNEP NENYP YNEPN NENPY
From this experiment I have found out that when the letter “P” is at the front of the name Penny then there are 12 different combinations. The same rule applies to the letters “E” and “Y” when they are at the front of the name Penny. But when the letter “N” is at the front of the name Penny then there are 24 different combinations.
Overall there are 60 different combinations for the name Penny.
I have now decided to investigate the number of different arrangements for the name Brian. From my previous experiments and their results I have made a prediction. My prediction is that there will be 120 different combinations for the name Brian. This is double the number of arrangements for the name Penny. I made this prediction because the factors that affect the number of arrangements are how many letters there are in the word and whether or not there are two or more of the same letter in the word. I have found out that the more letters there are in the word then the more arrangements there will be but if there is a repeated letter in the word then there will half the number of arrangements than a word with all different letters.
BRIAN BIRAN BANIR BNAIR RBAIN RAINB RNBIA ABNRI ARIBN AIRBN
BRINA BINAR BANRI BNIAR RBANI RINBA RNBAI ABIRN ARINB ANBRI
BRAIN BINRA BARNI BNIRA RABNI RINAB RNAIB ABINR AIBRN ANBIR
BRANI BIANR BARIN RBIAN RABIN RIBNA RNABI ARBIN AIBNR ANRIB
BRNIA BIARN BNRIA RBINA RANIB RIBAN ABRIN ARBNI AINBR ANRBI
BRNAI BAIRN BNRAI RBNIA RANBI RNIAB ABRNI ARNBI AINRB ANIRB
BIRNA BAINR BNARI RBNAI RAIBN RNIBA ABNIR ARNIB AIRNB ANIBR
IBRAN IRANB INRAB NRABI NIBAR
IBRNA IRABN INRBA NRBIA RIABN
IBNAR IABRN INABR NRBAI RIANB
IBNRA IARBN INARB NRIBA NBARI
IBARN IARNB NBRIA NRIAB NABIR
IBANR IABNR NBRAI NIRAB NABRI
IRBAN IANBR NBIAR NIRBA NARBI
IRBNA IANRB NBIRA NIARB NARIB
IRNAB INBAR NBAIR NIABR NAIRB
IRNBA INBRA NRAIB NIBRA NAIBR
From this experiment I have found out that there are 24 different combinations for each letter at the beginning of the name Brian.
Overall there are 120 different arrangements for the name Brian.
I will now investigate the different arrangements with smaller names with repeated letters and without. Because I have noticed that this fact has an effect on the outcome.
I have decided to look at the different arrangements for the name Tom.
TOM
TMO
MOT
MTO
OMT
OTM
From this experiment I have noticed that there are two different combinations for each letter at the start of the name Tom.
Overall there are six different arrangements for the name Tom.
