Solutions to 2009 Math Puzzles
Monthly Question: January 2009
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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