feb 22

1. We found the number of ways a slalom skier can go through the following courses:
   
   
   
   Here are the answers - 4, 6 and 8 ways:
   
   
   
2. We looked at the old puzzle in a new way. In a cafe frequented by dragons and unicorns, a bill was showing 3 cabbage heads and 3 apples. Recall that unicorns always eat 2 apples and a cabbage head, and dragons always take 2 cabbage heads and 1 apple each. How may dragons were there? The idea is draw a vector plane, with the horizontal steps representing cabbage heads, and vertical - apples. Each dragon eats a vector of (2,1) (two cabbages, one apple), and each unicorn eats (1,2). So, to get to (3,3) - three cabbages, three apples, shown as a purple point - one needs to make one "dragon step" and one "unicorn step":
   
3. We learned about the Roman numerals: IV is 4, but VI is 6... XLIX is 49!
   
   To remember: I is 1, V is 5, X is 10, L is 50, C is 100.

Homework:

1. How many ways are there to go down this course:
   



2. On the graph above, how many dragons and how many unicorns were eating at the cafe, if the bill was represented by the orange vector (5 cabbage heads, 7 apples)? yellow vector (8 cabbage heads, 7 apples)?
   
   
3. What are the numbers written in Roman numerals as XXIX? XIV? XXXIII?