Mystic Rose Poster
Problem
This poster is based on the problem Mystic Rose.
The poster is available as a PDF, or the image below can be clicked on to enlarge it.
Student Solutions
10 pointed mystic rose: 45 lines
100 pointed mystic rose: 4950 lines
Why?
Method 1 (Alison)
Start at the first point and draw one line to each of the 9 other points (9 lines).
The next point is already joined to the first point. Draw one line to each of the 8 remaining points (8 lines).
The next point is already joined to the first 2 points. Draw one line to each of the 7 remaining points (7 lines).
Continue.
Total lines: 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 lines
100 pointed mystic rose: 99 + 98 + 97 + ... + 11 + 10 + 45 lines (easier using method 2)
Method 2 (Charlie)
If you draw a line from one point to all of the others, you would draw 9 lines.
Doing this from all 10 points, you would get 90 lines.
But you would draw each line twice, once starting from each end.
So really there are only 45 lines.
For a 100 pointed mystic rose, there are 99$\times$100$\div$2 = 4950 lines.