SUMMARY: Mar/Apr 18 Brain Teasers

Mar/Apr ’18 Brain Teasers – SUMMARY

REMINDER: Answers in red.  Solvers (submitted/correct) in blue. (Forgive any omissions.) Comments in green. For further elaboration, feel free to ask! 

• 1. Using the digits 1 – 6 once each, what is the largest proper fraction (less than 1) that you can form? (E.g. 234/516 is bigger than 1/3, but one can do better.) Largest received 543/612 (.887), (Jim Waterman) followed closely by 543/621 (.874) (Alexis Avis)
  2. Using the digits 1 – 6 once each, what is the largest product that you can form? (E.g. 23 x 4516 is 103868)  541 x 632 = 341,912  (Jim Waterman, Alexis Avis)
  3. What about the other operations? What’s the largest sum, difference, and/or quotient you can form, using the digits 1 – 6 once each? 65432 + – / 1, respectively.  (Alexis Avis)
  4. Jack had a bag of 128 apples.  He sold 25 percent of them to Jill.  Next he sold 25 percent of those remaining to June.  Finally, he gave the shiniest one of those remaining to his teacher.  After that, how many did he have?  71 apples.  (Jim, Alexis, Amy Ragsdale).
  5. I have twice as many nickels as dimes.  If the value of my nickels is $5.00, what is the value of my dimes?  Also $5.  (Jim, Alexis).
  6. If 1 + 2 + 3 + . . . + m = 120, what is the value of m ?  15.  (Jim, Alexis, Amy). 
  7. You are facing northeast and make an about-face.  Which major direction is on your right? West.  (Alexis, Amy).
  8. Consider this string: 8 2 7 5 6 4 5 3 4.  If the difference between the first number and the fifth number is greater than the difference between the first number and the sixth number, respond with the number 7.  Otherwise, take the difference between the differences and respond with that number.  2.  (Jim, Alexis, Amy)
  9. In Boontown, streets that begin with a vowel run east-west, unless they also end with a vowel, in which case they run north-south.  Other streets can go either way.  Berkeley street is perpendicular to Alice street.  In which direction does Berkeley run? East/West. (Jim, Alexis, Amy)
  10. The volumes of Gibbon’s Decline and Fall of the Roman Empire stand side by side on a bookshelf (Vol I to the left of Vol II, etc).  A bookworm starts at page 1 of Volume I and bores his way in a straight line to the last page of Volume II.  If each cover is 1/8 inch thick, and each book with the covers is 2 inches thick, how far did the book worm travel? 1/4 inch. Note that Vol 1 is to the right of Vol II, so the work only goes through 2 covers. (Jim, Amy).  
  11. (An old classic!) A bear left its den and walked straight south for 1 mile.  Then it turned left (right angle) and walked another mile.  Finally it turned left again, and walked one more mile – arriving right back at its den!  What color was the bear – and why?  White.  The only way such conditions can happen is at the North Pole, hence polar bear.  (Amy – and Jim, if you want to tolerate his ‘usual’ answer.  🙂 ).
  12. The number 10 exceeds 25% of another number by 3.  What is the mystery number?  3.  (Jim, Amy).
  13. I’m a two-digit (positive, whole) number.  I’m one less than a multiple of 8 and three less than a multiple of 7.  What number could I be?  (At least two answers?)  39 & 95.  (Jim)

  BONUS(es):

  B1. Repeat #1 – #3 above, and in each case, replace the word largest with least.  Do any, some, or all.  Little interest here, understandably – turns out it’s pretty boring.  For more specific answers, contact me.
  B2. Something interesting happened at this year’s NCAA Basketball Tournament.  Arizona, a #4 seed, ended up being ‘the ultimate loser’ (for lack of a better term).  Arizona lost to Buffalo, which in turn lost to Kentucky, which in turn lost to Kansas State, which in turn lost to Loyola Chicago, which in turn lost to Michigan, which in turn lost to Champion Villanova!  Here’s your question:  How likely is that chain of events?  Will such a situation likely occur every year?  Yes, this situation will happen every year.  Note this seems ‘magical’, the way it’s stated.  Starting with the winner, however, and going the other direction makes it clear it will always happen.
  B3.  What is the answer to the Jason’s Jumble in our Foxtrot Cartoonfor today?  What’s the ‘deal’ with that answer? (What makes it funny?)  The computer scientist wrote his winnings in base 2, which makes his $64 look much bigger (1000000).  Mostly correct answer by Jim Waterman.