Introduction
A woman only has 10 and 20 pence coins to use in a phone box. I have to investigate the number of different ways she could use 10 and 20 pence coins in a phone box. I am also investigating a man who only has 10 and 50 pence coins. I will start off with the woman.
0 pence call
10=10p =1 way
20 pence call
20=10p+10p
20=20p =2 ways
30 pence call
30=10p+10p+10p
30=20p+10p =3 ways
30=10p+20p
40 pence call
40=10p+10p+10p+10p
40=20p+10p+10p
40=10p+20p+10p =5 ways
40=10p+10p+20p
40=20p+20p
50 pence call
50=10p+10p+10p+10p+10p
50=20p+10p+10p+10p
50=10p+20p+10p+10p
50=10p+10p+20p+10p =8ways
50=10p+10p+10p+20p
50=20p+20p+10p
50=20p+10p+20p
50=10p+20p+20p
Pascal´s triangle theory
This should help me to work out long and write out long equations like the ones I am doing
E.g. 50 5 10p =1
1 20p and 3 10p=4 =8 ways
2 20p and 1 10p=3
To get this I used the calculator button which has a big c you put the total number of units at the top then you put the number of 20 pence coins at the bottom. You use the biggest one at the bottom I use 20 pence because it is relevant. The way that Pascal made up this theory was he got a triangle and started with 1 at the top and started adding them up as he went down like this:
1
2 1
3 3 1
4 6 4 1
5 10 10 5 1
6 15 20 15 6 1
7 21 35 35 21 7 1
He did this for the rest of the way down. Instead of a calculator Pascal would have used the number of units added up to see how far he had to go down and the number of units in the biggest value to see how far he would of gone across.
E.g.50
5 10p =1
20p and 3 10p=4 down and 1 across
2 20p and 1 10p=3 down and 2 across
You then look at where the numbers would be on the triangle and add them up that would come to 1+4+3 which would equal 8.
Investigation
I am now going to use Pascal´s triangle in my investigation to shorten the length of my equations.
60 pence call
60= 6 10p =1
60=1 20p and 4 10p=5
60=2 20p and 2 20p=6
60=3 20p=1
This would equal 13 different combinations
70 pence call
70=7 10p=1
70=1 20p and 5 10p=6
70=2 20p and 3 10p=10
70=3 20p and 1 10p=4
This would equal 21 different combinations
80 pence call
80=8 10p=1
80=1 20p and 6 10p=7
80=2 20p and 4 10p=15
80=3 20p and 2 10p=10
80=4 20p=1
This would equal 34 different combinations
Results
This is a table of my results and a prediction for this far into this investigation
Cost of phone call 10 pence 20 pence 30 pence 40 pence 50 pence 60 pence 70 pence 80 pence
A woman only has 10 and 20 pence coins to use in a phone box. I have to investigate the number of different ways she could use 10 and 20 pence coins in a phone box. I am also investigating a man who only has 10 and 50 pence coins. I will start off with the woman.
0 pence call
10=10p =1 way
20 pence call
20=10p+10p
20=20p =2 ways
30 pence call
30=10p+10p+10p
30=20p+10p =3 ways
30=10p+20p
40 pence call
40=10p+10p+10p+10p
40=20p+10p+10p
40=10p+20p+10p =5 ways
40=10p+10p+20p
40=20p+20p
50 pence call
50=10p+10p+10p+10p+10p
50=20p+10p+10p+10p
50=10p+20p+10p+10p
50=10p+10p+20p+10p =8ways
50=10p+10p+10p+20p
50=20p+20p+10p
50=20p+10p+20p
50=10p+20p+20p
Pascal´s triangle theory
This should help me to work out long and write out long equations like the ones I am doing
E.g. 50 5 10p =1
1 20p and 3 10p=4 =8 ways
2 20p and 1 10p=3
To get this I used the calculator button which has a big c you put the total number of units at the top then you put the number of 20 pence coins at the bottom. You use the biggest one at the bottom I use 20 pence because it is relevant. The way that Pascal made up this theory was he got a triangle and started with 1 at the top and started adding them up as he went down like this:
1
2 1
3 3 1
4 6 4 1
5 10 10 5 1
6 15 20 15 6 1
7 21 35 35 21 7 1
He did this for the rest of the way down. Instead of a calculator Pascal would have used the number of units added up to see how far he had to go down and the number of units in the biggest value to see how far he would of gone across.
E.g.50
5 10p =1
20p and 3 10p=4 down and 1 across
2 20p and 1 10p=3 down and 2 across
You then look at where the numbers would be on the triangle and add them up that would come to 1+4+3 which would equal 8.
Investigation
I am now going to use Pascal´s triangle in my investigation to shorten the length of my equations.
60 pence call
60= 6 10p =1
60=1 20p and 4 10p=5
60=2 20p and 2 20p=6
60=3 20p=1
This would equal 13 different combinations
70 pence call
70=7 10p=1
70=1 20p and 5 10p=6
70=2 20p and 3 10p=10
70=3 20p and 1 10p=4
This would equal 21 different combinations
80 pence call
80=8 10p=1
80=1 20p and 6 10p=7
80=2 20p and 4 10p=15
80=3 20p and 2 10p=10
80=4 20p=1
This would equal 34 different combinations
Results
This is a table of my results and a prediction for this far into this investigation
Cost of phone call 10 pence 20 pence 30 pence 40 pence 50 pence 60 pence 70 pence 80 pence