May 5

• Warmup: 
• Devil offers another deal: each time you clap, he squares your amount of money, but then takes 99% away. How much you need to start with to actually profit from the deal?
• Find the remainder of 2222.....222/7 (1000 2's)
• Binary numbers: review what we know; algorithm of finding binary representations.
• Convert 2033 and 10001 into binary. Convert 1011110001 and 10000111101 into decimal.
• Adding numbers. Subtracting, multiplying...
• Binary numbers are longer than decimal, - by how much?

April 28

• Warmup: 
• Devil offers a deal: each time you clap, your amount of money doubles, - but you'll pay me $64. You agree, but after 3 claps all you had is gone! How much you started with? How much you need to start to grow richer and richer?
• Find a number consisting only of 1 and 0's which is divisible by 3. By 9. 
• What about numbers made of 8 and 5's?
• What about divisibility by 7? 1001. Remainders.
• Binary numbers: weights 1,2,4,8 etc: represent 1, 5, 14, 17... Adding numbers. Subtracting.
• More shear transformations. What transformations preserve shape?

April 21

• Warmup: 
• Adding 0 makes 2-digit number 252 bigger, - find the number
• Adding 0 between 2 digits makes it 9 times bigger
• Moving 9 from 1st to last (3rd) place increases the number by 216
• Number trick:
  x-> 3x-> 30x-> 30x-5-> 6x-1->6x+12->x+2->2 
• Design your own trick
• Coordinate system: shears
  S:(x,y)->(x+y,y) 
• Apply to squares and rectangles.
• U:(x,y)->(x,y-x).
• Find SU. Find SU^6.
• Game: card guessing?

April 14

• Warmup: 
• Homework: discuss oil/vinegar problem; moving candy into one place... 
• Three boxes: first has 6 less candies than 2nd and 3rd together; second has less candies than 1st and 3rd together. How many candies in the third box?
• Cop runs 3 times faster than a robber. Can cop spot the robber in a city of 4 square blocks (3 streets and 3 avenues)? 
• Periodic patterns: each 2x2 square on an infinite grid contain U D R C (unicorn, dragon, rabbit, cat). Is it true that each row or column contains all critters?
• Linear transformations: we know symmetries; what about shears?
  S:(x,y)->(x+y,y)Find images of a few points. Draw what happens to a cat.
• Do S^2. Find S^-1.