Larry Campbell Brain Teasers

Jan/Feb ’19 Brain Teasers

  1. (An oldie-but-goodie!  Too easy?)  I have two coins that add up to 55 cents, but one of them is not a nickel.  What are the coins?
  2.  How would you divide 55 such that one of the numbers is 1.5 times the other?  What are the two numbers?
  3. I fell off a 30 foot ladder and didn’t get injured.  How can this happen?
  4. The free-throw line on a HS basketball court is 12 feet across, and is a diameter of the half circle which appears above it on the court.  The rectangle below the line (going back to the end line)  is 12 x 19 feet.  (For a more detailed drawing, see FreeThrowLane. )  Together, these two make up the free-throw lane.  What is the perimeter of that figure?
  5. What is the area of the free-throw lane figure above?
  6. Find the 1053rd digit in the decimal expansion of 1/7.
  7. A jar is 1/4 full of marbles.  If 25 marbles are added to the jar, it becomes one-third full.  How many marbles does the jar hold when it’s full?
  8. A farmer came to town with some melons.  He sold half of them plus half a melon, and found that he had one whole melon left.  How many melons did he bring to town?
  9. (Sound familiar?) Can you put 50 coins into 10 envelopes so that each envelope contains a different number of coins?
  10. A man spends one fifth of the money in his wallet. He then spends one fifth of what remains in the wallet. He spends $36.00 in all.  How much money did he have to begin with?
  11. On a 3 x 3 grid, arrange the digits 1 – 9 (once each) in such a way that each row, each column, and each diagonal adds to 15.  (This is called a magic square.)
  12. Jeff Bezos is worth roughly $137 billion. A Mexican peso is worth approximately a nickel.  How many pesos is Jeff Bezos worth?  (Thanks to subscriber Susie Cook for this one.)

 
BONUS #1:  See the figure below.  How many squares (of any size) does it contain?  (FYI, the link “Click here to see answer” below does not work.  🙂 )
BONUS #2:  (A repeat?)  What’s the last digit (units place) of the product of the first 100 primes?

Figure for Bonus 1:

9 thoughts on “Jan/Feb ’19 Brain Teasers”

  1. 1. The one that is not a nickel is a half dollar. The other is the nickel.
    2. The numbers are 22 and 33.
    3. The ladder was lying on the ground still.

  4. Answer to squares is 27 if you count the outside square or 26 if you interpret “contain” as not including it.
    Answer to No. 3 is that you had the ladder horizontally on two saw horses only three foot high and you fell off that.
    The answer to NO. 9 is pathetic.

  5. #9 cannot be done. If the first envelope only gets one coin, the second envelope gets two coins, and so on until 9 envelopes have been filled with 9 different numbers of coins, you will have only 5 coins left since 1+2+3+4+5+6+7+8+9=45 and you started with 50 coins. Should have started with 55.
    #11 Top row of the magic square contains the numbers 4, 9, 2 (left to right). Middle row has 3, 5, 7. And the bottom row is 8, 1, 6.
    #12 Jeff Bezos is worth 2740 billion pesos. How poetic!

    1. Hi Frank!! I don’t usually post BT submissions while they’re still active, but in this case, I’ll make an exception, as it might be useful to everyone.
      YES, I’m aware that the link for ‘check the answer here’ doesn’t work. 🙂 Which is fine with me. 🙂 I tried to delete that when I posted it, but couldn’t. But since it doesn’t work anyway, I quite worrying about it.
      AND, I don’t usually give BT answers while they’re active, but in the case of the bonus, I will say simply “No, there are not exactly 33 squares.” (Whether there are more or less, I won’t yet say. 🙂 ).
      All details to follow in a mailing or two. THANKS!!

  7. 1. a quarter and a nickel (the OTHER coin)
    2. divide 55 by 2.5; numbers are
    22 & 33
    3. You weren’t at the top, you were near the bottom. OR Part of the ladder was submerged in water.
    4. approx. 68.85 ft. (or 50 + 6pi)
    5. approx. 113.1 sq. ft.
    (or 228 + 36pi)
    6. 1053rd digit is 2
    7. 300 marbles
    8. tricky wording, but if I’m not misinterpreting it he brought two and a half melons to town
    9. no, it’s not possible
    10. $100
    11. row 1: 2 4 9
    row 2: 6 8 1
    row 3: 7 3 5
    12. 2.74 x 10^12 or
    2 trillion, 740 billion pesos
    Bonus: 40 squares

  8. 1. The other one is a nickel.
    2. 22 and 33
    3. You were close to the ground.
    9. Starting with one envelope you put zero coins. In each of the remaining envelopes you put 1, 2, 3, 4, 5, 6, 7, 8, 9, coins.
    11. First row 4, 9, 2 Second row 3, 5, 7 and last row 8, 1, 6
    Bonus 1 36

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