Solutions to 2009 Math Puzzles

  • January 2009: Number Association
  • Februaary 2009: The Speed of Heinz Ketchup
  • March 2009: Why 0/0 is Undefined
  • April 2009: Can 1 = 2?
  • May 2009: An Odd Equation
  • June 2009: Cubic Meter Versus Cubic Yard
  • July 2009: A Tipping Problem
  • August 2009: Hockey and Probability
  • September 2009: If Life Was Measured In Heartbeats
  • October 2009: Log Averages

    2008 Puzzles


    Monthly Question: January 2009

    The question was:

    Which of the words below completes the following sequence?

    unicorn, compass, Rocket Richard or Gordie Howe,...

    A. a baker's dozen

    B. a pound of butter

    C. a box of donuts

    D. a liter of juice

    Solution

    The following numbers are associated with the given words:

    unicorn....number of horns = 1 = 12

    compass...# of principal directions = 4 = 22

    Rocket Richard.wore the # 9 = 32

    The next member of the series must be associated with 42 = 16

    So the answer is a pound of butter = 16 ounces


    Monthly Question: February 2009

    The question was:

    Estimate the average speed of ketchup that is flowing from the mouth of an upended bottle. Express your answer in miles per year.

    Solution

    (*inches/60sec)(3600s/h)(24h/day)(365.25 days/y)(ft/12 in)(mile/5280 ft)

    * using estimates that range from 1 to 3 inches per minute, we obtain an average speed in the range of 8 to 25 miles per year.

    .

    Monthly Question: March 2009

    The question was:

    Prove: 00 is undefined.

    Solution

    00= 0(n-n) where n =/= 0

    = 0n/0n

    But 0n = 0, and division by zero is undefined.


    Monthly Question: April 2009

    Here's a classic. The following seems to prove that 1 = 2. Every step seems legitimate, but where does the logic go astray ?

    Let a = b.

    a + a = a + b

    a + a - 2b = b + a - 2b

    2a - 2b = a - b

    2(a-b) = a - b

    2(a-b)/(a-b) = (a - b)/(a-b)

    2 = 1.

    Solution

    Since a = b. a-b = 0. So division by zero in the second laststep is not permitted.


    Monthly Question: May 2009

    Solve for x .

    3x + 3-x = 3.

    Solution

    Let u = 3x

    u + 1/u = 3

    u2 - 3u + 1 = 0.

    u = 2.62 or 0.38

    x = 0.88 or -0.88


    Monthly Question: June 2009

    The difference between a yard and a meter is about 3.37 inches.But if you are getting a cubic metre of cement as opposed to a cubic yard, how much more cement are you getting? Express your answer as a percent.

    Solution

    A cubic metre is about 39.37^3 = 61 023 cubic inches. A cubicyard is 36^3 = 46 656 cubic inches, a difference of 14 367 or about 31%.Those 3 inches make the cubic metre 31 % bigger than a cubic yard. Many amateur and some professional construction workers have learned this the hard way.


    Monthly Question: July 2009

    Your friend tells you that after a 14% tax on the original cost and after a 15% tip, also based on the original tab, he paid $20 for a meal. What was the menu price?

    Solution

    $20 is 129% of the original price, x. Thus x = 20/1.29 = $15.50


    Monthly Question: August 2009

    Given 19 hockey players , of which only 2 can play in nets, only 5 on defense and the rest only as forwards, how many possible lineups does a coach have to choose from? ( A lineup consists of a goalie, two defenceman, and three forwards; each forward is adaptable to either wingor center, and each defenceman can play either defensive wing)

    Solution

    12 X 11 X 10 X 5 X 4 X 2 = 52 800 lineups, enough to outlast their playing careers.


    Monthly Question: September 2009

    An elephant outlives a mouse by 73.5 years. But if life was measured in heartbeats, we'd have to say that a mouse lives as long as an elephant. This is because a mouse's heart beats 50 times faster than an elephant's. How long, then, does a mouse live?

    Solution

    The mouse lives 1.5 years.

    • 50rx =r(x + 73.5) where r = mouse's heart rate.
    • and x = mouse's lifespan.
    • 50x = x + 73.5
    • x = 1.5

    Monthly Question: October 2009

    If log x is the average of log Y and log Z, and Y >Z, how are Y and Z related to x?

    Solution

    log x = (log Y + log Z)/2

    2 log x = log Y + log Z

    log x2 = log Y + log Z

    log x2 = log YZ

    x2 = YZ,

    so x2 = (ax)(x/a)

    Y is some multiple of x

    And Z is x divided by that same multiple.

    (Think of 100, 1000 and 10 000.)





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