august 30

• Work out the cross problem: tile the plane; find an integer lattice; cut the cross. 
• What is the area of a square: 1, 4, 9,... But the cross's area is 5; how we can make a square of the area 5?
• Try the same trick with other pentaminos? P, T,  
• Take white and black stones, same number of each. Place them on a circle; find a place so that when you start from there and add 1 for each black stone, and subtract 1 for each white stone, you never go below 0...
• Try to do the trains (using the Boston Metro visualization widget)
• Slice of bread with two cuts can be split into 3 pieces. What about a bagel? A pretzel?

Homework

• A family is crossing a dark narrow bridge; at most two of them can cross at a time, and the family has just one flashlight. Mom can run across in 1 minute, dad in 2 minutes; son in 5 minutes and their pet sea lion in 6 minutes. Can they all cross the bridge for 13 minutes?
• Here is a solution (there are many!) of the cross puzzle.
  
  
  
  Can you cut and reassemble each of these two pentaminos, to get squares?

OK, train again: if it makes 100 miles per hour, how many miles it makes in 15 minutes? 30 minutes? 45 minutes? One hour and 15 minutes?