november 4

Homework:

• Is it possible to mark some cells in a 6x8 array with x's so that each row has exactly 3 x's and each column exactly 2 x's?
• Find all x such that |x|+|x-2|≤ 4.
• The side disks of a spool are twice the radius of the inner cylinder. If one pulls the line, which way the spool will roll? (There is no sliding.)

October 28

Homework

1. Buses stopping at Pete's home can take him either to math circle or to pool. Bus in each of these directions comes every ten minutes.
   Pete leaves home at random time (no one has a watch there!) and takes the first bus that appears. Yet, he goes to pool 4 times more frequently that to math circle. How is this possible?
2. Plot y=|x|-|x-2|.
3. Rope running along the equator (its length is 2πR, where R is the radius of the Earth - approximately 25,000 miles) is extended by 2 feet and lifted uniformly above the surface. Will a cat be able to squeeze beneath the rope?