SUMMARY: Solutions & Solvers, Jul/Aug ’21 BTs

by | Sep 2, 2021 | 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 on solutions, please feel free to ask! Consider the complement of any acute angle and the supplement of any obtuse angle.  Is one of those always bigger (which one?) or might they vary?

  1. Consider the complement of any acute angle and the supplement of any obtuse angle.  Is one of those always bigger (which one?) or might they vary? The answer could easily vary, depending on the angles chosen.  Rita Barger, Anita Dixon, Alexis Avis.
  2. Consider any positive rational number and that number’s square root. .  Is one of those always bigger (which one?) or might they vary? The answer could easily vary, depending on the number chosen.  (Square roots between 0 & 1 are bigger than the original number.)  Rita Barger, Anita Dixon, Alexis Avis.
  3. Your father.  Rita Barger, Anita Dixon, Alexis Avis, Dan Felshin, Pat Campbell
  4. Which two whole numbers with a sum of 50 will give the largest product?  Accepted answers of (25 & 25) or (24 & 26), depending on whether you assumed the numbers were distinct).  Rita Barger, Anita Dixon, Alexis Avis, Frank Green.
  5. Two (distinct) numbers are chosen at random from the set (2,3,5,7) and multiplied together.  How many of the possible products are odd?  Three of the (six) possible products are odd. Rita Barger, Anita Dixon, Frank Green
  6. Find the product: (1 – 1/2) * (1 – 1/3) * (1 – 1/4) * . . .  * (1 – 1/10)  1/10.  Anita Dixon
  7. Find the product of all the even integers between -25 and 25. The product is 0 (since 0 is an even integer between -25 and 25).  Rita Barger, Anita Dixon, Frank Green.
  8. If the radius of a circle is tripled, how much is the area of the circle increased?  The area is increased ninefold.  Rita Barger, Anita Dixon, Alexis Avis.
  9. In a strange house, there are 6 rugs and on each rug sits 6 six-legged tables.  On each table, there are 6 six-legged creatures.  What is the total number of creature legs in this silly story? 1296.  Rita Barger, Anita Dixon, Alexis Avis.
  10. The mean of all the primes between 40 and 50 is subtracted from the median of the same primes.  To two decimal places, what is the absolute value of the answer?  0.67  (The mean is 43.67, the median is 43.) Rita Barger, Anita Dixon, Frank Green.
  11. HELP!!  I thought certain I had added at least one BONUS to the Brain Teasers this time around, but either I never did, or it has disappeared in various revisions.  CAN YOU HELP ME?  Help me solve this riddle (send me the Bonus or let me know it was never there) – and receive credit for this Brain Teaser!!  Apparently I did NOT include a Bonus in this group.  (A first perhaps?)  Anita Dixon, Alexis Avis.
  12. Have you seen the US Post Office’s new stamp??!  Check in out here.  Imagine – a puzzle on a stamp!!  Decipher the message, and get your BT credit! (you can look it up of course, but it’ll be more fun if you don’t.)  More Than Meets the Eye.  (Check out the link.  The answer was cleverly hidden in the caption. 🙂 ).  Frank Green
  13.  I don’t buy this ‘Only for Genius’ stuff.  This one’s not hard – what goes where the ? is?? I took either 25 or 1 (depending on whether your viewed the ? as a product or a factor. Anita Dixon, Alexis Avis, Frank Green.
  14. The number 555,555 can be expressed as the product of two 3-digit numbers.  What is the smaller of those two? 715. Anita Dixon.
  15. Two standard dice are rolled.  What’s the probability (in fraction form) that the sum of the two numbers is prime? 15/36 (= 5/12). Frank Green. Alexis Avis

SUMMARY: Solutions & Solvers – May/June 21

by | Jul 9, 2021 | 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 on solutions, please feel free to ask! 

  1. This brain teaser first appeared on 5/3/21.  This is almost a ‘prime countdown day’.  a)  Why is it NOT?  b) When will the next true prime countdown day occur?  a) 1 is not a prime.  b) 7/5/32.  Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman
  2. What has a face and two hands, but no arms or legs?  A [non-digital] clock (or watch) face.  Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman, Frank Green, Marcia Morriset
  3. True or False? The sum of the reciprocals of the factors of 4 is greater than 2. False.  It adds to 1.75 (or 7/4, etc.) Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman.
  4. You are running a marathon and overtake the person in 2nd What place are you in now? 2nd. Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis,  Frank Green, Marcia Morriset
  5. One-fourth is one-third of what number? 3/4 Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman
  6. If 3x + 1 is an even number, what is the next larger even number?  3x + 3  Rita Barger, Amy Ragsdale, Anita Dixon, Jim Waterman, Frank Green
  7. Math Brain Teaser for Middle School Students D.  (10).  Rita Barger, Amy Ragsdale, Anita Dixon, Jim Waterman
  8. If p is an odd prime, find the sum of all the factors of 4p. 7p + 7  Rita Barger, Amy Ragsdale, Anita Dixon,
  9. SIMPLIFY:  7/22 ÷ 14/44  1.  (7/22 = 14/44) Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman, Frank Green, Marcia Morriset
  10. I thought of beekkeeping (or -er), but most had bookkeeper (-ing).  All would work, of course. Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman, Frank Green
  11. More English oddities:  ‘FACETIOUS’ is the only word in English which has this property.  Can you spot it (the property)?The word contains all 5 vowels, and in order.  (Jim Waterman pointed out that facetiously ALSO includes the y!) Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman, Frank Green
  12. The radius of Circle A and the diameter of Circle B are both 4 cm.  What is the ratio of the smaller circle’s area to the larger’s? 1:4 Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis, Jim Waterman, Frank Green
  13. Suppose John’s average heart rate is 72 beats/minute.  Given that, how many times would his heart beat in a day? 103,680. Rita Barger, Amy Ragsdale, Anita Dixon
  14. Pick ANY 6 negative integers.  Which is bigger – their sum or their product, or might it vary? The product, always.  (With six negatives, the product will always be positive, the sum negative.) Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis
  15. What is ¼ of 240?  (Keeping answer in exponent form is certainly acceptable – even advisable!) 238  Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis.

BONUS 1:  See #1.  There’s another fairly famous math entity we could connect in a ‘countdown’ to  5/3/21.  What is it, and when will the next one occur?  (Possible multiple answers?)  The digits are all Fibonacci numbers.  Next one would be 8/5/32.   Rita Barger, Anita Dixon

BONUS 2:  A circle of radius 8 is cut into a large plywood board.  Find the length of the side of the largest cube that will pass through the hole. 8*(SQRT2)  Amy Ragsdale, Anita Dixon, Jim Waterman 

BONUS 3:  See # 6.  What are the next two odd numbers after the original 3x + 1?  3x +2, 3x + 4.  Rita Barger,  Amy Ragsdale, Jim Waterman 

BONUS 4:  If x*y = the product of x and y, and x#y = x – y, then find [2(8#12)] # [(3*2)#5]  – 9. (-8 # 1 = -8 – 1 = -9) Rita Barger, Amy Ragsdale, Anita Dixon

Brain Teasers – Jul/Aug 2021

by | Jul 9, 2021 | Brain Teasers | 0 comments

NOTE:  Newest BTs in red, Bonuses in blue, comments in green, updates in purple.

  1. Consider the complement of any acute angle and the supplement of any obtuse angle.  Is one of those always bigger (which one?) or might they vary?
  2. Consider any positive rational number and that number’s square root. .  Is one of those always bigger (which one?) or might they vary?
  4. Which two whole numbers with a sum of 50 will give the largest product?
  5. Two (distinct) numbers are chosen at random from the set (2,3,5,7) and multiplied together.  How many of the possible products are odd?
  6. Find the product: (1 – 1/2) * (1 – 1/3) * (1 – 1/4) * . . .  * (1 – 1/10)
  7. Find the product of all the even integers between -25 and 25. 
  8. If the radius of a circle is tripled, how much is the area of the circle increased?
  9. In a strange house, there are 6 rugs and on each rug sits 6 six-legged tables.  On each table, there are 6 six-legged creatures.  What is the total number of creature legs in this silly story?
  10. The mean of all the primes between 40 and 50 is subtracted from the median of the same primes.  To two decimal places, what is the absolute value of the answer?
  11. HELP!!  I thought certain I had added at least one BONUS to the Brain Teasers this time around, but either I never did, or it has disappeared in various revisions.  CAN YOU HELP ME?  Help me solve this riddle (send me the Bonus or let me know it was never there) – and receive credit for this Brain Teaser!!
  12. Have you seen the US Post Office’s new stamp??!  Check in out here.  Imagine – a puzzle on a stamp!!  Decipher the message, and get your BT credit! (you can look it up of course, but it’ll be more fun if you don’t.)
  13.  I don’t buy this ‘Only for Genius’ stuff.  This one’s not hard – what goes where the ? is??
  14. The number 555,555 can be expressed as the product of two 3-digit numbers.  What is the smaller of those two?
  15. Two standard dice are rolled.  What’s the probability (in fraction form) that the sum of the two numbers is prime?

 

Possible Zoom Topics

by | May 16, 2021 | AfterMath Adventures - Fun/Learning, Various Answers | 0 comments

Possible Fun One-Shot Zoom Topics

Designed to be fun, and to fit in your hectic schedules, here are some possible topics that could surface at AME in the near future. All of these would be short (30-40 minutes), with time for questions. 

Interesting & Weird Mathematicians – And Stories About Them!  A standing ovation for a talk where no words were spoken?!  The ultimate interesting and WEIRD mathematician!  What there is no Nobel Prize in math.  Napier’s psychic rooster?!  And many, many more!!   Likely a Part 1 and a Part 2 (at least?)

Lewis & Clark on the Missouri River  A quick summary – with pictures of the places – of some of the Corp of Discovery’s adventures (good and bad) on the Missouri River part of their 3-year journey.

Spitballs From the Back Row  A collection of stories and anecdotes from in/near the classroom (including some of my own mishaps!), with some brief discussion of how we can learn from them.  Likely a Part 1 and a Part 2.

Brief ‘Snapshot Travelogues’  If you like the Photo of the Week in the Mailings, you should like this adventure.  We’ll focus on a country, OR a region of the US, or a similar attribute, and focus there for awhile.  Likely a dozen or more possibilities here!

And others are on the ‘drawing board’ at this very moment!

I’d LOVE to hear if anything above ‘grabs you’, as well as any preferences, suggestions (day of week, time of day, other topics?).  EITHER leave a COMMENT below, or use the CONTACT  FORM ,or simply REPLY to the Mailing.  Input always appreciated!

May/June ’21 Brain Teasers

by | May 1, 2021 | Brain Teasers | 6 comments

NOTE:  Newest BTs in red, Bonuses in blue, comments in green, updates in purple.

  1. This brain teaser first appeared on 5/3/21.  This is almost a ‘prime countdown day’.  a)  Why is it NOT?  b) When will the next true prime countdown day occur?
  2. What has a face and two hands, but no arms or legs?
  3. True or False? The sum of the reciprocals of the factors of 4 is greater than 2.
  4. You are running a marathon and overtake the person in 2nd What place are you in now?
  5. One-fourth is one-third of what number?
  6. If 3x + 1 is an even number, what is the next larger even number?
  7. Math Brain Teaser for Middle School Students
  8. If p is an odd prime, find the sum of all the factors of 4p. 
  9. SIMPLIFY:  7/22 ÷ 14/44
  11. More English oddities:  ‘FACETIOUS’ is the only word in English which has this property.  Can you spot it (the property)?
  12. The radius of Circle A and the diameter of Circle B are both 4 cm.  What is the ratio of the smaller circle’s area to the larger’s?
  13. Suppose John’s average heart rate is 72 beats/minute.  Given that, how many times would his heart beat in a day?
  14. Pick ANY 6 negative integers.  Which is bigger – their sum or their product, or might it vary?
  15. What is ¼ of 240?  (Keeping answer in exponent form is certainly acceptable – even advisable!)

BONUS 1:  See #1.  There’s another fairly famous math entity we could connect in a ‘countdown’ to  5/3/21.  What is it, and when will the next one occur?  (Possible multiple answers?)  

BONUS 2:  A circle of radius 8 is cut into a large plywood board.  Find the length of the side of the largest cube that will pass through the hole.

BONUS 3:  See # 6.  What are the next two odd numbers after the original 3x + 1?

BONUS 4:  If x*y = the product of x and y, and x#y = x – y, then find [2(8#12)] # [(3*2)#5]