SUMMARY: Solutions & Solvers – Jan/Feb ’20 BTs

by | Mar 6, 2020 | Brain Teasers, Various Answers | 0 comments

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 is the value of this fraction?  (6 – 9 x 7) / (6 + 4 x 3)  -57/18, or -3 1/6.  (Don’t forget order of operations.)  Frank Green, Amy Ragsdale
  2. A palindrome is a number that reads the same forwards and backwards.  How many palindromes are there between 1 & 100? 9 (11, 22, . . . 99)   Frank Green, Amy Ragsdale, Alexis Avis
  3. A group of teenagers went into a fast-food restaurant. They each bought exactly the same thing and their total bill was $44.11.  How many were in the group? 11 (Only # dividing amount evenly.)  Frank Green, Amy Ragsdale, Alexis Avis
  4. How many whole numbers are between the square roots of 8 and 80? 6 (3, 4, . . . 8)  Frank Green, Amy Ragsdale, Alexis Avis
  5. The average score of 6 tests is 93 (on a scale of 0 – 100).  What is the lowest possible grade on any one test? 58  Frank Green, Amy Ragsdale, Alexis Avis
  6. The sides of a triangle are 8, 15, and 17 units.  If each side is doubled, what is the area of the new triangle? 240  Frank Green, Amy Ragsdale, Don Hayes
  7.  Consider the spellings of the counting numbers. A) What number is the first to contain the letter ‘a’?  One thousand. Amy Ragsdale, Alexis Avis  B) What is the only number to be spelled in alphabetical order ? Forty Alexis Avis  C) Same as B, but reverse alphabetical order? One Frank Green, Alexis Avis
  8.   The 22nd and 24th Presidents of the US had the same mother and father, but were not brothers?  How can this be? Same person – Grover Cleveland  (Only President to serve two non-consecutive terms.  Benjamin Harrison served the term in between.)  Frank Green, Amy Ragsdale, Alexis Avis
  9.  Can there ever be two consecutive months with a Friday the 13th?  (Why?) Yes, it can happen in a non-leap year in Feb/Mar. (Feb has 28 days in those years, so exactly 4 weeks, so Feb’s numbering starts again in March.) Otherwise, NO.   Frank Green, Amy Ragsdale, Alexis Avis
  10. The Feb 10 Mailing mentions Year Product Days  (See Wild Cards or Item 4 of this link.)   As mentioned, 2018 has (exactly) 5 of these special dates. A)  What are the 5 YPDs this year? 1/20/20, 2/10, 4/5, 5/4, 10/2 Amy Ragsdale, Alexis Avis  B) Is this the FIRST year this century with (exactly) 5? No.  2018 also had exactly 5.  C) 2012 had 6 YPDs.  Have there been others since then? No.  (The next year with [exactly] 6 is 2030.)
  11. There are five (5) sisters on the main floor of the house, and they are the only ones home..  Ann is reading, Margaret is cooking, Katy is playing chess, and Marie is doing laundry.  What is the fifth sister doing?  Playing chess with Katy! Frank Green, Amy Ragsdale, Alexis Avis
  12. I simply don’t believe the “95%”.  I’ll bet many of you can get it!

Assuming the same view from every angle, making each of the 4 levels a square, there would be 16 + 9 + 4 + 1 = 25 balls.  Frank Green.  Granted, picture is slightly misleading, so alternate explanation(s) considered, but none matched interpretation(s).

*********

For the first time in over 5 years, no one submitted a solution (correct or not) to any Bonus problem! COLOR ME BLUE 🙁  I’ll probably carry at least some of them over.

BONUS 1:  Refer to the humorous ‘proof’ that all numbers are interesting.   The technique used there won’t work in the infinite case (no ‘smallest’ number necessarily!)  Can you think of a similar approach to the ‘proof’ that would work?

BONUS 2: Refer to #2 above.  How many palindromes are there between 100 and 1000?

BONUS 3: Refer to #10 above.  Are there any YPDs in any century with seven (7) or more YPDs?

BONUS 4:

Summary: Solutions & Solvers – Fall ’19 BTs

by | Nov 26, 2019 | Various Answers | 0 comments

Fall ’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. I recently cleaned out my MSU ‘Emeritus’ office (whew!).  I found two items tacked to a bulletin board. One was Hampton’s Travel Tips #628. The other was a coupon for a drawing, and was numbered 9998896.  Knowing my fascination with numbers, why might I have saved each of these?  (LOTS of possible answers here, of course, and most will receive credit.)  628 is formed from the first 2 perfect numbers (6 & 28).  9998896 can be turned upside down and still reads as a number. (To this day, I’m still not SURE which was the ticket number!)  One or both parts: Rita Barger.                       
  2. Perhaps you’ll remember KrazyPic1 from Aug 26.  Assuming all 4 ‘highlighted’ digits there are used once-each in a 4-number code, how many possible codes are possible? 24  Rita Barger, Amy Ragsdale.
  3. Name two consecutive prime numbers whose product is 899. 29 & 31.  Rita Barger, Amy Ragsdale, Don Hayes.
  4. What starts today, can’t be found at noon, and is required to end sunset?  The intended answer is ‘the letter t’, but Rita Barger submitted ‘darkness’, which I LOVE!!  Rita Barger, Amy Ragsdale, Don Hayes, Frank Green.
  5. Melissa went to dinner with Andrew, George, and Ulysses.  She ate along, but they all showed up to pay for the meal.  Why? Andrew Jackson, George Washington, and Ulysses S. Grant are faces on the bills she used to pay for the meal. Rita Barger, Amy Ragsdale, Frank Green.
  6. Which number is the third smallest of these?  0.3, 3.03, 0.303, 3.3303, 3.303  Rita Barger, Amy Ragsdale, Frank Green.
  7. Find the sum of the digits of the largest even 5-digit number that is not changed when its ones and ten-thousands digits are interchanged. 43 (for 89998) Frank Green. Partial credit – Amy Ragsdale.
  8. If there are four cars ahead of a car, four cars behind a car, and a car in the middle, what is the fewest number of cars in the line? 5 Frank Green, Amy Ragsdale.
  9. (Is this a repeat?) What three letters can be arranged to describe a beverage, a verb, and a homonym? Tea, eat, ate. (Perhaps that should read homophone?) Frank Green, Amy Ragsdale, Don Hayes. 
  10. 1/5 ÷ 1/5 ÷ 1/5 ÷ 1/5 = ? 25  Frank Green, Amy Ragsdale.
  11. Find a palindrome that is a cubic number less than 2000. 1331 = 11^3.  Amy Ragsdale, Don Hayes.  (Amy R notes I provided a clue by making this problem #11.  :-).  Was that intentional, she wonders.  I’ll never tell.)
  12. How can you plant ten seeds in eight rows with three seeds in each row? Plant them in a 3 x 3 grid, and using all directions, there will be eight rows of three. No correct submissions.
  13. (Repeat) Using each of the ten digits once, find two five-digit numbers with the greatest possible product. Several close answers here.  Amy Ragsdale’s 97530 x 86421 = 8,428,640,130 is largest received, but not officially verified as ‘largest’.
  14. (Repeat) What’s a good method to quickly solve this problem mentally?   (2019 + 2019) x 50  It’s 2*2019*50.  Group the 2*50 to get 100 and 100*2019 = 20190. Amy Ragsdale.
  15. (Repeat) What part of a half square foot is a half foot square?  A half ‘square foot’ is 0.5 ft^2.  A ‘half foot’ squared (or a square of side half-foot) is 0.5*0.5, or 0.25 ft^2.  So the latter is half the former in size.  No correct submissions.
  16. (Repeat) How many cards must you draw from a deck of 52 cards to be sure that at least two are from the same suit? 5.  No correct submissions.

 

BONUS 1:  We’ve done several variations of the billiard ball/counterfeit coin problem recently.  Here’s a most interesting new one (at least to me):  You have the usual 12 counterfeit coins, and now you know that TWO of them are counterfeit and are too heavy (but both ‘bad’ coins weigh the same.).  Can you determine/identify BOTH the bad coins in five (or less) weighings with the same balance scale? Yes, it can be done.  Details provided upon request.  Don Hayes

BONUS 2: For real math nerds!  🙂  How many pairs of integers p and q exist such that (p^2+1)/q and
(q^2+1)/p are both integers? (Shared by Don Hayes, who says he saw it in a movie.)  Don Hayes and Amy Ragsdale each provided or have solutions.  Details upon request.

BONUS 3:  Arrange the integers from 1 – 16 in such a way that the sum of any two consecutive integers is also a square. 8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9, 16.  Amy Ragsdale.  (Other than reversing direction, I know of no other ways this can be done.)

BONUS 4:  See #12 above.  The source I used for this problem says “ten seeds in ten rows”.  I’m not sure I believe it?!  (I can get 8 rows, so I changed wording, but . . .).  Can anyone help out?

CREATIVITY BONUS A:    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!)

CREATIVITY BONUS B:  Submit a good Creativity Bonus idea for this section!!  

Summary: Solutions and Solvers: Summer ’19 BTs

by | Sep 6, 2019 | Brain Teasers, Various Answers | 0 comments

Summer ’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! 

NOTE:  Solvers of at least one BT: Frank Green, Rita Barger, Jim Waterman, Alexis Avis, Jennifer Steele, Kathy Gordon, Dan Felshin, Kay Buckley, Amy Ragsdale, Kurt Killion

  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.)  Frank Green, Rita Barger, Jim Waterman, Alexis Avis, Jennifer Steele, Kathy Gordon, Kay Buckley, Amy Ragsdale.
  2. What do female elephants have that no other animals have? Baby elephants. Frank Green, Rita Barger, Jim Waterman, Alexis Avis, Jennifer Steele, Kathy Gordon, Amy Ragsdale.
  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, Jim Waterman, Alexis Avis, Jennifer Steele, Kathy Gordon, Amy Ragsdale.
  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. One or more parts: Frank Green, Rita Barger, Jim Waterman, Alexis Avis, Jennifer Steele, Kathy Gordon, Amy Ragsdale.
  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   Rita Barger, Alexis Avis, Kathy Gordon
  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).  Frank Green, Rita Barger, Alexis Avis, Kathy Gordon
  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   Frank Green, Rita Barger,  Amy Ragsdale
  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,  Alexis Avis, Amy Ragsdale
  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 Frank Green, Rita Barger,  Alexis Avis, Amy Ragsdale
  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 Frank Green, Rita Barger,  Alexis Avis, Amy Ragsdale
  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 Frank Green, Rita Barger, Amy Ragsdale
  12. In any given leap year, what date marks the 2/3 point of the year? Aug 31  Frank Green, Rita Barger, Amy Ragsdale
  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) Frank Green, Rita Barger, Amy Ragsdale
  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, Amy Ragsdale
  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 Amy Ragsdale, Frank Green, Amy Ragsdale
  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? Bill, at 13.  (Al is 12 and Carl is 8).  Amy Ragsdale

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.  Solvers of B1 and at least one part of B2 were Rita Barger, Jennifer Steele, Kathy Gordon, Amy Ragsdale.

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.  Only solver was Amy Ragsdale, who cleverly noticed that after  weighing 9 balls on each side, and determining the heavier side, one could then proceed exactly as in Bonus 2B above.  🙂 

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 and Amy Ragsdale.

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.  (LOTS of ‘right’ answers, of course!!  We had two submissions last month [see MarMaySolutions ].  Let’s get some more!!) Update:  See Comments below, (and my note there) for current submissions for this Bonus.  Kurt Killion added a contribution during this period.  His and other contributions can be seen in the COMMENT section of the Brain Teasers.

No submissions for EITHER B or C below.  I’m sad.  🙁   We’ll probably extend these one more time.  Won’t ANYONE have some fun with us?

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!) CREATIVITY BONUS C:  Submit a good Creativity Bonus idea for this section!!  

Summary: Solutions & Solvers – Mar/Apr/May 19

by | May 30, 2019 | Brain Teasers, Various Answers | 0 comments

Mar – May ’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! 

NOTE:  Solvers of at least one BT:  Frank Green, Kathy Gordon, Rita Barger, Don Hayes, Amy Ragsdale, Jennifer Steele, Alexis Avis, Jim Waterman, and Anita Dixon.

  1. In 1982, T.R. Benker set a joke-telling record.  He told jokes continuously for 1803 minutes.  How much longer than one day did he tell jokes? 6 hours, 3 minutes longer than one day. Kathy Gordon, Rita Barger, Amy Ragsdale, Jennifer Steele, Alexis Avis, Jim Waterman.  Partial credit to Frank Green.
  2. The widest street in the world is the Monumental Axis in Brasilia, Brazil.  It has 6 lanes and is 0.25 kilometers wide.  If 1 meter = 1.1 yards, how wide is the street in feet?  825 ft. Frank Green, Rita Barger, Amy Ragsdale,  Alexis Avis
  3. What is the least common multiple of 54 and 81? 162 How about the greatest common divisor of 16, 41, and 198? 1  Frank, Green, Kathy Gordon, Rita Barger, Amy Ragsdale, Jennifer Steele 
  4. (A repeat from May ’17) You have 10 consecutive integers.  The sum of the first 3 is 39.  What is the sum of the last two? 41  Kathy Gordon, Rita Barger, Amy Ragsdale, Jennifer Steele, Alexis Avis
  5. Variations on a oft-repeated theme:  a)  Find a proper fraction between 3/7 and 4/9. LOTS(an infinite number) of right answers.  275/630, 43/100, 55/126, . . .  b) Note that if I just added numerators and denominators, I’d get 7/16.  Is 7/16 a solution also?  YES.  Kathy Gordon, Rita Barger, Amy Ragsdale.
  6. Of the first 10 counting numbers, three of them have an odd number of factors.  Find the sum of these three numbers. 14 (= 1 + 4 + 9)  Kathy Gordon, Rita Barger, Amy Ragsdale
  7. Of the first 25 counting numbers, how many of them have an odd number of factors? 5. (1,4,9,16,25)  Kathy Gordon, Rita Barger, Amy Ragsdale
  8. Goldbach’s Conjecture  states (in one equivalent variation) that every even integer greater than 2 can be written as the sum of two primes. Verify this is so for the even integers from 10 to 20. Variety of correct ‘verifications’ here. Kathy Gordon, Rita Barger, Amy Ragsdale       (Bonus Bonus: Prove or disprove this Conjecture in general, and A) win an autographed copy of each of my books, and B) make us both famous! 🙂 ). Sadly, no proofs/disproofs here.  I was hoping we’d be famous! (Lest you wonder:  this is one of the classic unknown problems in what’s called Number Theory.)
  9. If the day before yesterday is the 23rd, what is the day after tomorrow?  the 27th.  Kathy Gordon, Rita Barger, Amy Ragsdale
  10. See Pic 1 below.  I have one solution for this, but I’m not sure I like it.  Can someone else get others?  GREAT FUN HERE!!  FOUR different answers that work!!  See figure below.  Kathy Gordon, Rita Barger, Amy Ragsdale, Don Hayes, Anita Dixon. (Am I missing someone[s] here? 🙁    Sorry!!)
  11. See Pic 2 below (and clarification there).  I’m kinda doubting the ‘90% fail answer’.  If you remember your order of operations, this should be a piece of cake!  12  Kathy Gordon, Rita Barger, Amy Ragsdale
  12. Find the largest fraction that a) has a denominator of 17, and b) when added to 1/3, keeps a sum less than 1. 11/17.  Kathy Gordon, Amy Ragsdale, Rita Barger
  13. If a certain book is 4th from the left on a bookshelf, and also 6th from the right on the same shelf, how many books are on the shelf?  9.  Kathy Gordon, Amy Ragsdale, Rita Barger
  14. (Repeat?) How can you throw a ball as hard as you can and have it come back to you, even if it doesn’t bounce off anything? There is nothing attached to it, and no one else catches or throws it back to you. Throw it straight up. Kathy Gordon, Amy Ragsdale, Rita Barger
  15. What is impossibl,e to hold for an hour, even though it hardly weighs anything? Your breath. Kathy Gordon, Rita Barger
  16. How many times can you take 3 from 96? Only once.  (After that you’re taking it from 93, 90, etc.) Rita Barger, partial credit to Kathy Gordon.

BONUS #1:  (Ongoing)  What’s the last digit (units place) of the product of the first 100 primes?  0.  (The product of the first 3 primes (2,3,5) is 30.  After that, all future products will retain the 0.)  Rita Barger, Amy Ragsdale.

BONUS #2:  What else do you notice about the numbers you found in #7?  They are perfect squares (among other things).  Kathy Gordon, Amy Ragsdale.

CREATIVITY BONUS #3:  Make as long of a sentence as you can (at least 5 words?) where every word starts with the same letter.  (LOTS of ‘right’ answers, of course!!  Should be fun!)            

Rita Barger’s submission: Arthur, Ann, Alex, Avery, and Arabella are all alert, ambitious, ambidextrous, alarmed, adopted actors actively attracting albatrosses and arresting aardvarks.

Amy Ragsdale’s submission:  Many mischievous monkeys merrily made myriad mango marmalade Monday morning.

BONUS #4:  The grades on six tests are all on a 0 – 100 scale, inclusive.  If the average for the six tests is 93, what’s the lowest possible grade on any one test (in order to maintain the 93 average)? 58.  Kathy Gordon, Rita Barger.

Pic 1:  For #10 above.  Possible Answers: (Are there others?)

  1.  Rotate horizontal match on 6 up to become 0.   0 + 4 = 4.
  2.  Move vertical match on plus sign to 6, making it 8. 8 – 4 = 4.
  3.  Move lower vertical match on 6 (making it 5) to the top of the 4 (making it 9)  5 + 4 = 9.
  4.  Move vertical match on plus sign, putting on top of equal sign.  6 – 4 =/ (does not equal) 4.  

Pic 2:  For #11 above.

(NOTE:  Let’s assume there is a + sign at the end of 1st 2 rows.  Thanks to Amy Ragsdale for noticing!)

Summary: Solutions & Solvers – Jan/Feb 19 BTs

by | Mar 22, 2019 | Brain Teasers, Various Answers | 0 comments

Jan/Feb ’19 Brain Teasers – SUMMARY

REMINDER: 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. (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?  A nickel and half dollar.  (One coin is NOT a nickel – the other is.)  Frank Green, Kathy Gordon, Rita Barger, Amy Ragsdale, Marcia Morriset, Jennifer Steele.       
  2.  How would you divide 55 such that one of the numbers is 1.5 times the other?  What are the two numbers?  22 & 33.  Frank Green, Kathy Gordon, Rita Barger, Amy Ragsdale, Jennifer Steele.          
  3. I fell off a 30 foot ladder and didn’t get injured.  How can this happen?  Fell off bottom rung OR ladder was horizontal OR ladder partially submerged in water, among others.  Frank Green, Kathy Gordon, Rita Barger, Amy Ragsdale, Marcia Morriset, Jennifer Steele, Dan Felshin.                           
  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?  6*(PI) + 50 ft.  (app 68.8 ft)  Frank Green, Amy Ragsdale.  (Close:  Rita Barger, Kathy Gordon.)                                                                                             
  5. What is the area of the free-throw lane figure above?  18*(PI) + 228 sq. ft.  (app 285.4 sq. ft)         Frank Green. (Close:  Rita Barger, Kathy Gordon, Amy Ragsdale.)                                                                          
  6. Find the 1053rd digit in the decimal expansion of 1/7. 2.  Amy Ragsdale.                                                                
  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? 300 marbles. Rita Barger, Amy Ragsdale.                                      
  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?  3 melons. Rita Barger.                              
  9. (Sound familiar?) Can you put 50 coins into 10 envelopes so that each envelope contains a different number of coins?  Depending on conditions, A) impossible, or B) multiple solutions.  Credit to Frank Green, Rita Barger, Don Hayes.  (Two [or more] recent columns dealt with this problem and a personal anecdote involving Marilyn vos Savant.  To (re-)read, see 50Coins1 and/or 50Coins2.)   
  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?  $100.  Rita Barger, Amy Ragsdale.                                                                                                                                                                
  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.)  LOTS of answers here. Just one is shown below Problem #12 below.  Frank Green, Rita Barger, Amy Ragsdale, Jennifer Steele.                              
  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.)  2.74 trillion  OR 2 trillion, 740 billion.  Frank Green, Amy Ragsdale.  (Partial credit to Rita Barger.)                                   

One answer to #11:

Image result for 3x3 magic square

 

 

 

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.  🙂 )  There are 40 squares*.  Rita Barger, Amy Ragsdale (Partial credit to Marcia Morriset.)

BONUS #2:  (A repeat?)  What’s the last digit (units place) of the product of the first 100 primes?  Carried over to next set of BTs.  Correct solution by Amy Ragsdale.

Figure for Bonus 1:

* There are 18 (16 + 2) 1×1 squares, 9 2×2 squares, 4 3×3 squares, 1 4×4 square (the big one), and 8 ‘half unit squares.’  Holler if questions.

Summary, Solvers, and Solutions: Nov/Dec ’18 BTs

by | Jan 27, 2019 | Brain Teasers, Various Answers | 0 comments

Sep/Oct ’18 Brain Teasers – SUMMARY

REMINDER: 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.  Check out this Krazy Pic from the 10/29 mailing.  Why do we know this picture probably came from Great Britain, say, rather than the US? (I just noticed there is ALSO another subtle semi-clue – anyone catch it?)  The most likely clue is the British spelling of the word ‘colour’.  (The other subtle clue is the character on the sign is Andy Capp, a British cartoon character. [The strip was popular in US, too.]  Rita Barger, Kathy Gordon, Jennifer Steele.

2.  Check out this riddle.  Interesting, and ‘outside the box’.  (I’d probably change the question to ‘of the four names here, which is most likely . . .’, but hey.) The lady’s six children contain the first six notes of the musical scale: Do, Re, . . .  So following that pattern, the likely choice is Ti(tus). Rita Barger, Frank Green.

3.  J.J.J. Smith has an 85 average on his four tests in Calculus.  The final is the same weight as each test – all are 100 points.  What will he need to score on the final, to bring his grade up to an A (90 average)? It can’t be done (with 100 point tests.)  [He has 340 points now.  For a 90 average on 5 tests, he’d need a total of 450, or 110 more points.] This is a classic example of the adage “you can’t average averages”.  Rita Barger, Kathy Gordon.

4. If you write down every whole number (integer) between 500 and 700, how many times will you write the digit 6?  140 times. Rita Barger, Jennifer Steele.

5.  I’m Rodney and I live on a farm.  With me are 4 other dogs named Brownie, Spot, Fido, and Blackie. There is a fifth dog – what is it’s name?  Rodney.  🙂 Rita Barger, Kathy Gordon, Jennifer Steele Frank Green.

6.  Ralph went for 5 days without sleep. (He felt and acted perfectly normal.  Why is that? He slept fine at night. Rita Barger, Kathy Gordon, Frank Green.

7.  How is your mother’s sister’s brother in law related to you? More than likely, your father.  (“Uncle” is also possible in some circumstances, and credit was given for that.) Rita Barger, Kathy Gordon, Jennifer Steele.

8.  Always, sometimes, or never?  A)  A right triangle has an acute angle. Always.  B) A right triangle has an obtuse angle. Never. Rita Barger, Kathy Gordon, Jennifer Steele, Frank Green.

9.  Always, sometimes, or never:  A)  The radius of a circle is longer than the diameter. Never.  B)  A triangle with 2 equal sides is equilateral.  Sometimes. Rita Barger, Kathy Gordon, Frank Green.

10. If p is a prime and  2p – 1 is also prime, then 2p – 1 is called a Mersenne Prime.  Find the three smallest Mersenne primes. 3, 7, 31.  (So much more that could be said here, but . . .) Rita Barger, Kathy Gordon.

11.  I am divisible by 5 and I am odd.  I have less than 4 digits, but am greater than 12 x 12.  The sum of my digits is a square and their product is 15.  What number am I?  315. Rita Barger, Kathy Gordon, Frank Green

12.  Find the area and perimeter of a right triangle with legs of 4 & 5. (Apologies all around.  I meant to say legs of 3 & 4, making it a classic 3,4,5 rt. triangle, and therefore a much easier problem. My brain and my fingers were not in sync, apparently.)  Area = 10 (sq units), Perimeter = 9 + SQRT(41). Rita Barger (with partial credit to Kathy Gordon [one part correct, slippery error on other], and Frank Green [who solved the problem I intended. 🙂 ] )