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The course work is about finding all the possible combinations for putting in to pay phones.

Extracts from this document...

Introduction

Pg1image00.png

The course work is about finding all the possible combinations for putting in to pay phones. Using different coins and using those results to try and find a formula that works so you would successfully be able to predict how many coins you would have into the pay phone to find out the next total without going through all the different listings. There are three parts to this coursework, the first two parts are an investigation into specific coins used and after the first two investigations there is a formula that works for whose coins. The third investigation is a more general case. The first two investigations help you with the third.  

10p

    |There is only 1combination of putting a 10p piece into a pay phone.

10p

20p

    For the 20p piece there is 2 combinations of putting a 20p piece into a pay phone.

        20p       10p, 10p

    pg2                      

30p         there is 3 different combinations

        For 30p to go into a pay phone.

        10p10p10p     20p10p         10p20p

Pg2

40p

        There are 5 different combinations of putting 40p into a pay phone.

        10p10p10p10p

                                20p20p

                               10p10p10p

                                20p10p10p      

        10p20p10p

50p

        There are 8 combinations for 50p and they are

...read more.

Middle

        20p20p10p10p

        10p20p20p10p

        20p20p20p

My prediction is correct 13 ways for 60p by using

The formula.

Table of resultspg4

Amount        No. of ways

10p        1

20p        2

30p        3

40p        5

50p        8

60p        13

        That’s my table of results

Investigation 2             pg5

This is an investigation to show the different combinations of putting in a 10p and 50p into a pay phone and seeing if there is any pattern that forms from the results. From this pattern I will try and find a formula. In this investigation I have started the call cost from 40p as I assume that if I started with a 10p, the first three results would all be the same, as 50p would be redundant in any call less than 50p therefore the data that I have found out for the first three results would be useless and the formula would be incorrect.

40p

      10p10p10p10p

There is 1 combination for 40p

50p

        10p10p10p10p10p

        50p

There are 2 combinations for 50p.

60p                                                   pg6

         50p10p

          10p50p

          10p10p10p10p10p10p

There are 3 combinations for 60p.    

70p

       10p10p10p10p10p10p10p

50p10p10p

10p50p10p

10p10p50p

There are 4 combinations for 70p

80p

...read more.

Conclusion

10p50p10p10p10p10p10p10p10p

50p10p10p10p10p10p10p10p10p

50p10p10p10p50p

10p50p10p10p50p        10p50p10p50p10p

10p10p50p10p50p              10p50p10p10p50p

10p10p10p50p50p        50p50p10p10p10p

10p10p50p50p10p                50p10p50p10p10p

10p50p50p10p10p

There are 20 sequences that prove that my formula is correct.        

General Investigation

Pg11

I have found that my formula relate to the coin used.

        Tn = Tn –1 + Tn -5

        -1 = 10p used

           -5 = 50p used

So for any formula using coins you could use the formula.

              Tn = Tn – x + Tn –y

X and y being the coins used in the formula.

This is also true of the first formula using 10p and 20p coins.

The theory will only work if both the coin values used a 10p coin and a 1.00£ in the formula.

Tn = Tn –1 + Tn –10

Would not work cause it has to be a prime number to work as with x and y formula, unless both x and y are prime numbers  it will not work.

pg12image01.png

I have found out the formulas for the pay phone problem and I have investigated further and found out that prime numbers are very important in the pay phone problem

        By Danny James Dawson

...read more.

This student written piece of work is one of many that can be found in our GCSE Pay Phone Problem section.

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