Larry Campbell Brain Teasers, Various Answers

SUMMARY: Solutions & Solvers – May/June ’20 BTs

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

  1. What kind of cheese is made backwards? 🙂  Edam.  Frank Green, Rita Barger, Amy Ragsdale, Barbara Blue
  2. What word begins and ends with ‘e’, but only has one letter? Envelope.  Frank Green, Amy Ragsdale, Barbara Blue, Don Hayes, Jim Waterman
  3. The integer 1234 is not divisible by 11. By re-arranging the digits, can you find one or more integers that are divisible by 11?  (A yes/no answer does not get full credit. 🙂 ). Yes, there are several.  1243 is one, for example. Frank Green, Rita Barger, Amy Ragsdale, Barbara Blue, Don Hayes, Jim Waterman
  4. A new-born infant was given 1 trillion dollars at birth.  (Wow!).  How much would he/she have to spend (average) each day to use all the money in 80 years (assuming no interest accrued)? Over 34 million!  ($34,223,134.84, to be exact.) Frank Green, Amy Ragsdale, Barbara Blue, Jim Waterman
  5. How many spherical meatballs of radius 1 can you make from a spherical meatball of radius 3?  Exactly 27. Rita Barger, Amy Ragsdale, Barbara Blue,  Jim Waterman
  6. (Repeat) The sum of A & B is 112.  A is 4 more than C, and B is 2 less than C.  What does C equal? 55  Frank Green, Amy Ragsdale, Barbara Blue
  7. I am < 25.  My ones digit is twice my tens digit and the digits add to an even number.  What am I? 24  Frank Green, Amy Ragsdale, Barbara Blue
  8. Find the shaded region (circle inscribed in a square) - YouTubeFind the area of the shaded region to the right.  –> 400 – 100*PI (sq cm). (Or roughly 85.9, if you prefer) Frank Green, Amy Ragsdale.
  9. Take any 3 consecutive integers.  Square the middle one and multiply the outer two together.  Try this several times and see what you notice.  Can you formulate a rule? The middle number squared is always one more than the product of the other two.  Frank Green, Amy Ragsdale, Don Hayes
  10. Peggy is writing down the integers from 1 to 1000. (Who knows?) She stops to rest after writing 630 digits. What is the last integer she wrote? 246  Amy Ragsdale
  11. I am an odd integer.  If you take away one letter from my name, I become even.  What am I?  SEVEN.      Frank Green, Amy Ragsdale
  12. When is it possible to subtract 1 from 19 and get 20?  When is half of 13 = 8?  With Roman numerals. Take one from IXX and you have XX.  Cut XIII in half (horizontally) and you have VIII left.      Amy Ragsdale
  13. How many prime factors does 2020 have, and what are they? 3 prime factors.  (2, 5, and 101)  Frank Green, Amy Ragsdale
  14. How many two-digit integers are divisible by either 3 or 5?  42        Frank Green
  15. Find 14232 – 14182. (You can probably crank this out fairly easily [?], but there’s a clever way to do it very quickly.)   14205   Frank Green, Amy Ragsdale
  16. What is the closest positive number (not just integer) to 0? There is NO such ‘closest’ number to 0. (Isn’t math amazing?!) Amy Ragsdale, Partial credit – Frank Green, 

 
BONUS 1:  Ten ping-pong balls are numbered from 1 to 10.  If two balls are drawn at random, what is the most likely sum of the numbers on the balls? (this can be done with knowing any probability.)  11. (Five different possible ways, more than any other sum.) Frank Green, Amy Ragsdale, Barb Blue
BONUS 2:  See #8 above. Re-label the 20 cm distance to a more general x cm.  Find an expression for the area of the shaded region. (3/4)*x^2*PI (sq cm) Frank Green, Amy Ragsdale
BONUS 3:  Every red card at an auto show was a sports car.  Half of all blue cards were sports cars.  Half of all sports cars were red.  There were 44 blue cars and 30 red cars.  How many sports cars were neither red nor blue. 8   Frank Green
BONUS 4:  Can you find a ‘fraction’ (one integer/another) whose decimal equivalent is the (ever-repeating) .3434343434  . . . ?  34/99  Amy Ragsdale
BONUS 5:  See #9 above.  If you have conjectured a ‘rule’ here, can you prove it?  One approach: Let the 3 numbers be x-1, x, x+1.  Then x^2 – 1 = (x+1)*(x-1).  Amy Ragsdale, Don Hayes
BONUS 6:  See #13 above.  How many total factors does 2020 have?  (and what are they?  That’s not a trivial question.  There’s actually a way to know how many w/out figuring them and counting directly.  Isn’t math wonderful? 🙂 ). There are 12 total factors.  (1,2,4,5,10,20,101,202,404,505,1010, and 2020)      Frank Green, Amy Ragsdale   

2 thoughts on “SUMMARY: Solutions & Solvers – May/June ’20 BTs”

  1. Was this an ‘x-tra’ tough run of BTs??
    Just saying, even with the answers, my head is still spinning a bit!
    Nevertheless, thank you (?)for the mental gymnastics!

    1. Hi Christine!! Not sure how to answer, of course. “Tough” and “Easy” are usually ‘eye of the beholder’ terms, eh?
      I hadn’t really noticed it myself – I had about the same number of respondents and at least one or two new ones. (But that always varies, too.) Plus, there always seem to be fewer and fewer responses as the answer period goes on. (Lots of early replies, fewer near the end.)
      I appreciate the input!! I’m always trying to lure new (and old) solvers and tread the fine line between fun and ‘too hard’. And to keep up as much variety as possible.
      Hopefully, you’ll like this next batch better? 🙂
      Larryu

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