Larry Campbell Brain Teasers

Brain Teasers 15-13 – September 2015

Posted 9/7:  Three”Real World” Brain Teasers Where Math Can Help 🙂

  1. Ralph found an ad for a lot that was advertised as ‘one acre by one-half acre’ in a marvelous location at a reasonable cost, yet he was a little reluctant to follow through.  Why?
  2. A professional sports team was in salary cap trouble.  The General Manager approached the team’s star, Willy Ketchem, with the following offer:  Please help us out this year by taking a 25% pay cut for this next year only.  If you’ll do that, we promise to give you a 30% raise the following year.  Willy was willing (say that three times quickly!), but his agent advised against it – for mathematical reasons.  Why is that?
  3. Why are manhole covers round?  Wouldn’t rectangular ones be easier to build? (There is an important mathematical reason for this!)

Added 9/14:  A couple of more traditional goodies:
4.   A car dealer sold 60 cars during a six-day sale.  Each day, he sold 4 more cars than he did the day before.  How many cars did he sell on              the first day?
5.  Which has more area – a square of side 1, or a circle with diameter 1?
Added 9/21:  BTs concerning Time Zones 🙂
6.  When it comes to time zones, the countries of China and India share an interesting fascinating fact.  What is it?
7.   How do time zones work at the North and South Poles, where all the longitude lines converge?
8.   And, finally, how does the International Space Station keep its time?
Added 9/21: Special Dates
9.  a)  What was mathematically special about the second Saturday of this month (9/12)?   b)  This phenomenon will occur only ONCE more this century!  When?  Why is it the last?

 Submit Answers!  There are NO tests and the answers are NOT graded, so lighten up!  If you want to submit  your answers to any or all of these, PLEASE feel free to do so!!  
You can always do this 3 ways:  1)  Use the Leave A Reply section below (though I may not make it public until after the deadline);   2) reply to (or contact) me directly by e-mail or by replying to any Weekly Sharing; or 3) by using the Contact Form link.   Your anonymity is protected for all formats (but only until submission deadline for the Leave a Reply format. )
Reminder:  Official deadline for  ALL BT submissions in  September  is noon Thursday, Sep 24. (Late submissions accepted if Answer Sheet hasn’t been prepared, but no promises.)

4 thoughts on “Brain Teasers 15-13 – September 2015”

  1. I am sure you already know this (and you you may not want to push your readers too far) but I like the extension to #3 that asks if there are other shapes that would work as well as a circle (at not falling down the hole).

  2. BT September 2105
    1. One acre by one half acre is nonsensical; an acre is an area not a linear dimension. There is something wrong with the deal.
    2.
    (1) He receives currently C salary.
    (2) Upon signing the contract he will get 3/4 x C.
    (3) The following year he will get 3/4 C + 1/3 X 3/4 C = 3/4 C + 1/4 C= 4/4 C= 1C.
    Conclusion: In the following year he will not get a raise from the current salary, he will simply get
    the current salary. This is not a good deal. In the long run he loses 0.25 X C of one year’s salary.
    3. Rectangle lids can drop through the rectangle holes; round lids cannot drop through the round holes.
    4. 40 (40 + 4+ 4+ 4+ 4+ 4 = 60).
    5. square = 1 (1 squared). circle = 1/2 squared X 3.14159 = 0.78789. The area of the square is larger.

  3. #2 Bad deal: If he signs the contract he will receive 0.75 X (X = current salary). The following year he will receive 0.75 X + 0.3 (0.75 X) = 0.975 X. He will end up with a total reduction in salary over the 2 years.

  4. According to the Chinese students we’ve had as International Friends from MSU, China has a single time zone. Therefore, some of the Chinese residents simply have to get used to the idea that it is dark at 1 p.m. in parts of their country while it is light at 1 p.m. in other parts. So, during Standard Time in the U.S., China is 13 hours ahead of our time . . . everywhere in China.

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