Sunday, February 13, 2011

Sunday, Febrauary 13, 2011

Problems are inspired by the Grade 9 text book today!
  • Typically, in bikes (cycles), there is a plastic reflecting light which is attached to a wheel, so that the bike is visible to a car coming across. What  will be the shape of the path traversed by this light, when the bike moves along?
  • Mr. Forget started  to walk back to his home from the grocery store, located 650 mts from his home. He started to walk back in the direction of his house, but went 800 mts, then suddenly remembers that he has gone past, and switches direction, and then walks back half the distance this time (400 mts), OOPS, he again remembers and then switches direction and walks back, and this continues .. Will he ever reach his home?
  • What is the total distance a puck travels in a hockey game? How will go about estimating this distance.  Ice rink is 200ft by 85 ft?  Assume that the hockey game is 60 minutes long, an average pass is approximately 15ft.
  • You  take a very long string, and double it up, then redouble it, then reredouble it, and so on. Lets say you did it 50 times. Now cut the string from the middle. How many pieces will you get?
  • How will you show that the sum of three consecutive numbers is divisible by 3. Can one make the same statement for 4 consecutive numbers being divisble by 4 and so on. It of course doesn't work for two.
  • Lets do some fun experiments with the Mobius strip. Take a ribbon, twist and then tape it. Mark the center line - and cut along, see what happens?  What if you have two lines - say 1/3rd and 2/3rd away and then cut along them, and see what happens?
  • Half of a fraction, decreased by 0.75 results in 7/12. What was the fraction?
  • How many different bracelets can be made consisting of 2 red and 3 green beads?
  • What is the smallest and largest possible value of a/b + c/d, where a,b,c,d need to take values from {1,2,3,4}?
  • What will be the last digit in 2^1234?

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