Mystic Rose
2) The mystic rose looks like many things. It can be described as a circle that has a star inside it; the number of lines on the star increases as the number of points around the circle increases.
3) Both Alison and Charlie are right as their methods both give the same correct answer.
Alison’s Method
10 point mystic rose = 9+8+7+6+5+4+3+2+1=45
Alison takes the number of points which is 10 and subtracts 1 from it to get nine. She then adds all the numbers from 1 to nine together to get her answer.
For example if the mystic rose had 5 pints around the circle the calculation would look like this;
5-1=4
4+3+2+1=10
Charlie’s method
Charlie takes the number of points around the circle and multiplies that by 1 less than it. He then halves it to get his answer.
10x(10-1)=
10x9=
90/2=45
4)
Number of Points Alison’s method Charlie’s method
4 3+2+1=6 (4x3)÷2=6
5 4+3+2+1=10 (5x4) ÷2=10
6 5+4+3+2+1=15 (6x5) ÷2=15
7 6+5+4+3+2+1=21 (7x6) ÷2=21
8 7+6+5+4+3+2+1=28 (8x7) ÷2=28
9 8+7+6+5+4+3+2+1=36 (9x8) ÷2=36
10 9+8+7+6+5+4+3+2+1=45 (10x9) ÷2=45
5) The advantage of Alison’s method is that it uses simple addition and therefore can be worked out easily. The advantage of Charlie’s method is that it can be solved quickly.
6)The number of points around the circle relates to what term it is . A circle with 4 points on it circumference is the 4rth term in the sequence.
Term 4 5 6 7 8 9 10
6 10 15 21 28 36 45
4 5 6 7 8 9
1 1 1 1 1
½=0.5
6 10 15 21 28 36 45
8 12.5 18 24.5 32 40.5 50
-2 -2.5
-3 -3.5 4 4.5 5
All these numbers in this row are half n
Nth term=( 0.5n2)- 0.5n
(n2 –n)÷2
7) 100=10000-100=9900÷2=4950
8)
4851=99 points
6214 = no answer
3655=86
7626=124
8656=no answer