Summary: Solutions and Solvers: Summer ’23 (and ’19) BTs

Summer ’23 (and ’19) Brain Teasers – SUMMARY

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. A man is walking his three dogs when he meets his brother who is walking his two dogs.  How many feet are there in total when they meet?  24 (Solutions which distinguised between ‘paws’ and ‘feet’ were noted, and given credit as appropriate.)  Rita Barger, Carmelita Tieskotter
2. What do female elephants have that no other animals have? Baby elephants. Rita Barger
3. Sammy was a real bookworm who spent all his time in the local library.  In just one month he worked his way through three volumes of an encyclopedia, and two volumes of a dictionary, yet he could not remember one word that they contained.  Why was that? As it says, Sammy is a real bookworm, so . . .Rita Barger
4. (Partial repeat) T or F?  A)  If the sum of two numbers is even, then both numbers are even.  B)  If the product of two numbers is even, then both numbers are even.  C)  A number with 5 factors is always bigger than a number with 4 factors. All three FALSE. Rita Barger
5. Many of you are familiar with my love of palindromes, especially when they appear on the odometer.  Very recently, I ran into an interesting situation.  I saw TWO palindromes two miles apart, and then realized that I wouldn’t see another one for 1100 miles!!  Given those circumstances, what are the three palindromes? The first two: 99,999 and 100,001. 1100 miles later: 101,101   No correct answers submitted.
6. What makes the number 8,549,176,320 unique?  Hint 1:  Don’t look for anything terribly ‘mathematical’ here.  Hint 2:  The answer might be different in other countries. The digits are in alphabetical order (spelling).  Rita Barger, with partial credit to Carmelita Tieskotter
7. (Via Cherry Hinderberger).  In the classic “Twelve Days of Christmas” song (swans, geese, pear tree, etc.) how many total gifts are given over the twelve days? 364   Rita Barger
8. A club containing 10 members decides to elect a President and a VP.  a)  How many slates of officers are possible? 90 b)  How does that number change if they also elect a Sec/Treas (one office)? 720 Rita Barger
9. (This week’s new BTs [9 – 12] are repeats from 2015 & 2016.)  Let’s suppose your heart beats 70 times/minute..  How many times will it beat in August? 3,124,800 Rita Barger
10. The average (mean) of 3 tests is 74.  What score is required on the 4th test to raise the test average to 78? 90 Rita Barger, Carmelita Tieskotter
11. Find the sum of the reciprocals of whole-number factors of 24.  (Remember ‘reciprocals’?  For example, the reciprocal of 7 is 1/7.) 2.5 Rita Barger
12. In any given leap year, what date marks the 2/3 point of the year? Aug 31 Rita Barger, Carmelita Tieskotter
13. Miss Korn collected coins and referred to her collections with interesting nicknames.  Her penny collection she called Cu, and her nickels collection, she called Ni.  What do you think she called her collection of silver dollars? Ag (The chemical abbreviation for silver) Carmelita Tieskotter
14. In a recent column (Twain, Teams, and Turf) we referred to five different entities (schools, parents, religion, society, and government) involved in our broader education and looked more closely at at the four (4) pairs of those teams involving schools.  Out of those 5 entities, however, how many total pairs  of teams are there? 10 pairs Rita Barger, Carmelita Tieskotter
15. I open my mathematics book, and the page numbers that face me have a product of 1806.  What are the two page numbers? 42 & 43 Rita Barger, Carmelita Tieskotter
16. The sum of the ages of Al and Bill is 25.  The sum of the ages of Al and Carl is 20.  The sum of the ages of Bill and Carl is 21.  Who is the oldest of the three and how old is he? A discrepancy/typo rendered confusing answers. Rita Barger, Carmelita Tieskotter – both  correct for the version they solved.
17. A recent Crossword Puzzle indirectly led to this Brain Teaser:  What do the following phrases all have in common:   “Goldwyn Pictures”, “folding brackets”, “tumbledown shack”, “crazy stupid love”, and “rhyming couplets”  Each phrase has NO repeated letters.  (I also took “they each have 15 letters”).  Rita Barger.
18. See Pic below. (The two figures are 170 and 130 cm, left to right.) 150 cm.  No correct answers submitted.
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BONUS 1:  I have seven billiard balls, one of which weighs less than the other six. Otherwise, they all look exactly the same. How can I identify the one that weighs less on a balance scale, using that scale no more than two times?  See B2 below.

BONUS 2:  Exactly the same situation as Bonus 1, only now you have A) 8, and B) 9 billiard balls.  Can you do either/both parts?  Bonus 1 and both parts of Bonus 2 CAN be done  Ask for details if desired.  Rita Barger.

BONUS 3:  See B1 and B2 above, with same conditions except that you now get THREE weighings.  Is it possible to achieve the same goal if there are 18 billiard balls?  Make your argument either way.(Demonstrate for, or argue against.) I somehow left out the above part (in red) all this time. If needed, I’ll carry this bonus forward into next time. This can also be done.  Rita Barger.

BONUS 4:  See #14 above.  Of the five entities there, how many TOTAL teams of any number (pairs and teams of 3, 4, or 5) are there? 26 total teams of 2, 3, 4, or 5.    Rita Barger

CREATIVITY BONUS A (Ongoing):  Make as long of a sentence as you can (at least 5 words?) where every word starts with the same letter.  Rita Barger and Carmelita Tieskotter.

Rita’s sentence:  After arriving at Arlington Aquarium, and after alerting appropriate authorities, and fter actively and aggressively asking Asa, Anthony, and Andrew about an annual academic arithmetic argument, Andy, Ariel, Arthur, Alan, Amy, Abby, Adrian, Agatha, Alaina and Ava arose and ambled away.

Carmelita’s sentence:  Currently Carmelita’s credit card company confirms Carmelita’s compulsive chocolate chip cookie consumption, concluding Carmelita, confessed chocoholic, cannot count calories conscientiously.

CREATIVITY BONUS B:  The Herman cartoon below has had the caption (temporarily) removed.  Submit your own caption and get us laughing!!  (Later, we may decide we like some of these submissions better than the original!)   Rita’s caption:  Your job was to advertise the circus, not join it.

Original caption was something like:  I think you’ll fit well in our accounting department.

CREATIVITY BONUS C:  Submit a good Creativity Bonus idea for this section!!  Rita:  Create a pattern of numbers that hasn’t been created before.