SUMMARY: Solutions & Solvers, Mar/Apr ’21 BTs

by | Apr 30, 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, please feel free to ask! 

  1. Consider π, 3.14, and 22/7. Write them in order from smallest to largest, or, if any are equal, mark EQUAL in appropriate spots..3.14, π, 22/7.  Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Jonah Albertson.
  2. Are there any days this year (’21) where the day# times the month# = the year# [21]? Yes.   Jan 21, Mar 7, and July 3. Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Jonah Albertson, Alexis Avis
  3. When if ever, is 1/x  bigger than x? When x is between 0 & 1, or when x is less than -1.  Anita Dixon,  Jonah Albertson, Rita Barger.  Partial Credit:  Amy Ragsdale
  4. When, if ever, is a number less than its square?  When the number is less than 0 or greater than 1.  Anita Dixon, Rita Barger, Jonah Albertson. Partial Credit:  Alexis Avis and Amy Ragsdale
  5. See picture and question -> Accepted 6 or 8, depending on whether submitter thought the holes in front went all the way through (and counted them separately.)   Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis
  6. A cubic foot of air weighs 0.0765 pounds. What is the weight of the air in a 20 x 30 x 10 foot classroom? 459 lbs. Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis
  7. Halley’s Comet appeared in 1758, 1834, 1910, and 1986. When will it next appear? 2062.  (Appears every 76 years.) Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis
  8. If grasshoppers can jump 59 times their length, how far can a 1.5 inch grasshopper jump? 88.5 in. Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis
  9. This past Saturday was 4/3/21. Let’s call that a ‘countdown day’.  When will the next ‘countdown day’ happen?  May 4, 2032. [5/4/32) (Other clever variations also suggested.)  Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis
  10. A penny weighs approximately 0.1 ounce. Using that figure, how much would a ton of pennies be worth? $3,200. Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis
  11. What is the perimeter of a square that has the same area as a 4 cm x 9 cm rectangle? 24 cm. Anita Dixon, Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis
  12. Solve this equation it only it is an easy one give a try  C. (25) (in this case: in order, from left to right.) Anita Dixon, Rita Barger, Amy Ragsdale, Alexis Avis
  13. There are (at least) two 2-digit numbers that are equal to 7 times the sum of their digits. Find at least one of them.. 21, 42, 63, 84. Anita Dixon, Rita Barger, Amy Ragsdale
  14. Write the numeral for the number eight billion, forty thousand, two 8,000,040,002 Anita Dixon, Rita Barger, Amy Ragsdale, Alexis AvisBONUS 1 See # 13 above.  Can you  find more than two such numbers?  See above for others.  Amy Ragsdale, Anita Dixon. 

 BONUS 2  Note that it takes 6 syllables to pronounce Kansas City Royals. but only 5 to pronounce St. Louis Cardinals.  On the other hand pronouncing either New York Yankees or Boston Red Sox only takes 4 syllables.  Lets take Major League Baseball, and add NFL football teams for fun, as well.  What are the extremes on syllables for City and Mascot?  Hurriedly, I can think of one team that takes 7 syllables, and one team that only takes 3.  Can you find them?  Can you find teams with more than 7? Or less than 3? Teams found with 3 syllables:  New York Mets, New York Jets, Cleveland Browns, Tampa Rays(may not be full name?)  Teams with 7 syllables:  Arizona Diamondbacks, Philidelphia Eagles, Philadelphia Phillies, Indianapolis Colts.  Teams with 8 syllables:  San Francisco 49ers. Contributers: Amy Ragsdale, Frank Green, Alexis Avis, Steve & Bobbi Kneeshaw.

BONUS 3 Did you see Dean Martin’s Fun Fact involving 80 beers and your birth year?  🙂  Can you explain how it works? [See also note at link for more precise updates.]  Ask for details.  Amy Ragsdale, Anita Dixon.

BONUS 4  See #10.  How much would those pennies weigh?  (Be alert!)  A ton of pennies would weigh             a ton.  🙂 Amy Ragsdale, Anita Dixon.

Brain Teasers – March/April ’21

by | Mar 5, 2021 | Brain Teasers | 9 comments

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

  1. Consider π, 3.14, and 22/7. Write them in order from smallest to largest, or, if any are equal, mark EQUAL in appropriate spots..
  2. Are there any days this year (’21) where the day# times the month# = the year# [21]?
  3. When if ever, is 1/x  bigger than x? 
  4. When, if ever, is a number less than its square?  
  5. See picture and question ->
  6. A cubic foot of air weighs 0.0765 pounds. What is the weight of the air in a 20 x 30 x 10 foot classroom?
  7. Halley’s Comet appeared in 1758, 1834, 1910, and 1986. When will it next appear?
  8. If grasshoppers can jump 59 times their length, how far can a 1.5 inch grasshopper jump?
  9. This past Saturday was 4/3/21. Let’s call that a ‘countdown day’.  When will the next ‘countdown day’ happen?
  10. A penny weighs approximately 0.1 ounce. Using that figure, how much would a ton of pennies be worth?
  11. What is the perimeter of a square that has the same area as a 4 cm x 9 cm rectangle?
  12. Solve this equation it only it is an easy one give a try
  13. There are (at least) two 2-digit numbers that are equal to 7 times the sum of their digits. Find at least one of them.
  14. Write the numeral for the number eight billion, forty thousand, two.        BONUS 1 See # 13 above.  Can you  find more than two such numbers?

    BONUS 2  Note that it takes 6 syllables to pronounce Kansas City Royals. but only 5 to pronounce St. Louis Cardinals.  On the other hand pronouncing either New York Yankees or Boston Red Sox only takes 4 syllables.  Lets take Major League Baseball, and add NFL football teams for fun, as well.  What are the extremes on syllables for City and Mascot?  Hurriedly, I can think of one team that takes 7 syllables, and one team that only takes 3.  Can you find them?  Can you find teams with more than 7? Or less than 3? (Submitted already: 2 or 3 teams with 7, 2 or 3 teams with more than 7 and 2 or 3 with only 3.  Are we missing any?  Join the fun!)

    BONUS 3 Did you see Dean Martin’s Fun Fact involving 80 beers and your birth year?  🙂  Can you explain how it works? [See also note at link for more precise updates.]

    BONUS 4  See #10.  How much would those pennies weigh?  (Be alert!)

SUMMARY: Solutions & Solvers; Jan/Feb ’21 BTs

by | Mar 4, 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, please feel free to ask! 

  1. Why are some folks already looking forward to Jan 1, ’23 at 5:08:13?  The date lists the first 7 digits of the Fibonacci Sequence. (1,1,2,3,5,8,13,21,34, . . .) Rita Barger, Amy Ragsdale.
  2. What is an interesting feature of the three words job, polish, and herb? (Yes, probably lots of ‘correct’ answers.) They each have different meanings when capitalized. (Similar versions accepted.) Rita Barger, Amy Ragsdale, Frank Green.
  3. Find a number less than 100 that is increased by one-fifth of its value when its digits are reversed. 45 Rita Barger, Amy Ragsdale, Frank Green, Dan Felshin.
  4. You close your book, forgetting to put in a bookmark, but you remember (who knows why?) that the product of the pages is 16002. What were the page numbers? 126 & 127  Rita Barger, Amy Ragsdale.
  5. A square plot of 160 acres is surrounded by a fence of total length 2 miles. How large a square plot will a fence of four miles surround?  640 acres.  (Doubling one side of a square quadruples the area.)   Rita Barger, Amy Ragsdale, Don Hayes.
  6. In what order are the following digits? 0, 2, 3, 6, 7, 1, 9, 4, 5,  In reverse alphabetical order, considering the digits’ spellings.  Rita Barger, Amy Ragsdale.
  7. Al, Joe, Carl, and Dave were standing in line. Dave was not first, Joe was between Al and Carl.  Al was between Dave and Joe.  In what order were they standing? Carl, Joe, Al Dave. Rita Barger, Amy Ragsdale, Frank Green, Dan Felshin
  8. This BT is stated as a question, so let’s go with it. If you think the answer is YES, solve it.  If you think it is NO, tell why.His Ex-Wife - Chapter 21 - Wattpad NO, It cannot be solved.  Briefly, the sum of 3 odd numbers is never even. Rita Barger, Amy Ragsdale, Frank Green, Don Hayes, Dan Felshin
  9. 1 + 1 + 1 x 0 + 1 + 1 = ____4____ Rita Barger, Amy Ragsdale, Frank Green.
  10. 10.You have $6.60 in dimes and quarters (only).  If there are 36 coins how many quarters to you have? 16 dimes and 20 quarters. Rita Barger, Amy Ragsdale, Frank Green.
  11. What is exactly (in fraction form) the sum of ½ and ¼ ? 3/4. Rita Barger, Amy Ragsdale, Frank Green.
  12. Your “I Love Math” club contains 6 men and 4 women. How many different committees of 2 men and 3 women are possible?  60.  Amy Ragsdale.
  13. How many squares (of any size) are in the drawing below?  40  Rita Barger, Amy Ragsdale.
    Image preview
  14. X is Y’s brother, but Y is not X’s brother. Who is Y?  X’s sister!  Rita Barger, Amy Ragsdale, Frank Green.
  15. How many cards must you draw from a standard 52-card deck to be sure that at least two are from the same suit? 5. Rita Barger, Amy Ragsdale
  16. The missing digit is 8.  (These are the 1st 12 digits in the decimal representation of PI.) Rita Barger, Amy Ragsdale

 

BONUS 1:  See #13 above.  How many rectangles are in the picture.  (I don’t know this answer!  It just came up in the Fun With Math Class. I’d LOVE to hear your conjectures.[I’ve heard one already.])  118??  I’ve got question marks because this is a relatively new problem to me (proposed by Kurt Killion), so I don’t have an official answers.  HOWEVER, both Kurt Killion and Amy Ragsdale have come up with 118 now.  And, I’ve seen Kurt’s work and can’t find any flaws.  I may carry this over to next time to give others time to confirm 118, or come up with another answer (along with reasoning.)

BONUS 2:  See #15 above.  How many would you have to draw to make sure you had at least 2 hearts? 41.  Rita Barger, Amy Ragsdale

Brain Teasers – Jan/Feb 2021

by | Jan 9, 2021 | Brain Teasers | 7 comments

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

  1. Why are some folks already looking forward to Jan 1, ’23 at 5:08:13?
  2. What is an interesting feature of the three words job, polish, and herb? (Yes, probably lots of ‘correct’ answers.)
  3. Find a number less than 100 that is increased by one-fifth of its value when its digits are reversed.
  4. You close your book, forgetting to put in a bookmark, but you remember (who knows why?) that the product of the pages is 16002. What were the page numbers?
  5. A square plot of 160 acres is surrounded by a fence of total length 2 miles. How large a square plot will a fence of four miles surround?
  6. In what order are the following digits? 0, 2, 3, 6, 7, 1, 9, 4, 5,
  7. Al, Joe, Carl, and Dave were standing in line. Dave was not first, Joe was between Al and Carl.  Al was between Dave and Joe.  In what order were they standing?
  8. This BT is stated as a question, so let’s go with it. If you think the answer is YES, solve it.  If you think it is NO, tell why.His Ex-Wife - Chapter 21 - Wattpad
  9. 1 + 1 + 1 x 0 + 1 + 1 = ________
  10. 10.You have $6.60 in dimes and quarters (only).  If there are 36 coins how many quarters to you have?
  11. What is exactly (in fraction form) the sum of ½ and ¼ ?
  12. Your “I Love Math” club contains 6 men and 4 women. How many different committees of 2 men and 3 women are possible?
  13. How many squares (of any size) are in the drawing below?
    Image preview
  14. X is Y’s brother, but Y is not X’s brother. Who is Y?
  15. How many cards must you draw from a standard 52-card deck to be sure that at least two are from the same suit?

 

BONUS 1:  See #13 above.  How many rectangles are in the picture.  (I don’t know this answer!  It just came up in the Fun With Math Class. I’d LOVE to hear your conjectures.[I’ve heard one already.])

BONUS 2:  See #15 above.  How many would you have to draw to make sure you had at least 2 hearts?

SUMMARY: Solutions & Solvers, Fall ’20 BTs

by | Nov 28, 2020 | 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. Mary’s mother had three daughters. The first two were named April and May.  What was the name of the third daughter?  Mary.  Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis.
  2. A cheetah was clocked running 550 feet in 10 seconds. About how many miles per hour is that? 37.5 mph Frank Green, Amy Ragsdale, Alexis Avis. Partial credit – Rita Barger.
  3. Find a three-digit perfect square whose last two digits are its square root. 625 Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis.
  4. Ninety-six is 37.5% of what number? 256. Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis.
  5. What is a) the mean and b) the median of the first 10 prime numbers? a) 12  b) 12.9 Frank Green, Rita Barger,  Alexis Avis.  Partial credit – Amy Ragsdale.
  6. Two dates are called ‘reciprocal dates’ if, when written as fractions, each is the other’s reciprocal. E.g., October 6 (10/6) and June 10 (6/10) are reciprocal dates.  Not all dates have reciprocal dates (Sep 21, e.g.), and 12 days are their own  reciprocal dates. (6/6, e.g.)  In any given non-leap year how many days do NOT have reciprocal dates? 221 days.  Frank Green, Amy Ragsdale.
  7. A triangle’s hypotenuse is 13 units. One of the legs is 12.  What is the triangle’s area? 30 Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis.
  8. A history/culture trivia BT: Name a) the man and b) the woman who has/have appeared on the cover or TIME most often. (I mean, what is Google for, right?) a) Richard Nixon.  b)  The Virgin Mary, Lady Diana, or Hillary Clinton (apparently depending on your source). Frank Green, Alexis Avis. Partial credit – Amy Ragsdale.
  9. My double exceeds my half by 2. Who am I? 4/3  Rita Barger, Amy Ragsdale
  10. Find three consecutive integers whose sum (adition) equals their product (multiplication). 1,2,3  See Bonus 2 for more correct answers. Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis.
  11. Is it possible for a year to have two consecutive months with a Friday the 13th? Yes, but only in Feb/Mar of non-leap years. Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis.
  12. True or false?  An 8″ (radius) circular pizza has over twice as much pizza as a 6″ pizza of the same thickness.  (Partial credit for correct answer [only].  Full credit for explanation.) False.  Frank Green, Rita Barger, Amy Ragsdale.  Partial credit – Alexis Avis.
  13. (Repeat?) Can you find FIVE consecutive integers, none of which are prime?  Yes.  An infinite number of correct answers.  The FIRST set occurs at 23,24,25,26,27. Frank Green, Rita Barger, Amy Ragsdale, Alexis Avis.
  14. If you draw a card from a ‘normal’ 52-card deck (no jokers), what’s the probability that the card you draw will be EITHER a heart OR a king? 16/52 or 15/52 (depending on your usage of the word OR [inclusive or exclusive]) Frank Green, Amy Ragsdale.

Determine the value for “?” in the equations on the left. (Easier than it might look.)

 

 

15. (above)  16 or 17, depending on interpretation of icons in lines/quations 3 and 4.  (Amy Ragsdale cleverly noticed that there are two mugs each in line 3, but only one mug in line 4!) Frank Green, Rita Barger, Amy Ragsdale.

16. Did you see the GARFIELD cartoon (see 10/24 at link) shared recently (today, for some of you) ?  For an easy almost-freebie, how could the wish of the kid on TV have backfired on him? Multiple answers, but if the bad-at-math genie had said ‘that’s your three wishes’ or ‘you have ONE more wish’ or the like, he’d have lost a wish. Frank Green, Rita Barger, Amy Ragsdale.

VIRAL PUZZLE #mathpuzzle #viral #quiz17. Multiple interpretations taken.  One interpretation was to count the ‘crossing’ points, making the question mark = 4. Frank Green, Rita Barger, Amy Ragsdale.

18.

18. (above).  Frank Green noted there is no arithmetic sign here, but assuming addition, the digits (from upper left to lower right) are 0 (or blank), 9, and 0.Frank Green.

 

Bonus #1:  How many states’ names can you string together so that the last letter of one becomes the first letter of the next?  E.g., WyominG, GeorgiA,  AlaskA, , . . . etc.  (We’ll keep ongoing records here and everyone who sets, breaks, or ties a current record in a new way will be listed later.)  Amy Ragsdale found TWO strings of 12!  (Ask, if you wish to see them.)

Bonus #2:  See #10 above.  There are actually THREE sets of triplets that satisfy this condition.  Can you find the other two?  The three triplets are (1,2,3),  (-1,0, 1),  and (-1,-2,-3).  Frank Green, Rita Barger, and Amy Ragsdale

Bonus #3:  See #13 above.  What’s the largest such string (of non-prime [composite]) integers you can find?  (The focus here is on YOU.  Multiple correct answers possible.) Rita Barger found a string of 17.  Amy Ragsdale found strings of 13 and 19.

Fascinating Math Fact:  It turns out here you can find a string of any length you want!!  If you want to find a string of 1000 whole numbers without a prime in it, you can do it!! A million? Check.  Any arbitrary (whole) number you want!!   (And it’s relatively ‘easy’ to demonstrate.)  In my mind, one of the Five (Maybe 6) Most Fascinating Facts in Mathematics!!  🙂

Bonus #4:  See #17 above.  What other attritbute(s) does/do the 3 numbers there share?  (Guess what?  Multiple answers possible.)  Assuming the answer of 4 above, all 3 numbers are perfect squares.  (Among other attributes.)  Amy Ragsdale.

Brain Teasers – Sep/Oct 2020

by | Sep 5, 2020 | Brain Teasers | 3 comments

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

  1. Mary’s mother had three daughters. The first two were named April and May.  What was the name of the third daughter?
  2. A cheetah was clocked running 550 feet in 10 seconds. About how many miles per hour is that?
  3. Find a three-digit perfect square whose last two digits are its square root.
  4. Ninety-six is 37.5% of what number?
  5. What is a) the mean and b) the median of the first 10 prime numbers?
  6. Two dates are called ‘reciprocal dates’ if, when written as fractions, each is the other’s reciprocal. E.g., October 6 (10/6) and June 10 (6/10) are reciprocal dates.  Not all dates have reciprocal dates (Sep 21, e.g.), and 12 days are their own  reciprocal dates. (6/6, e.g.)  In any given non-leap year how many days do NOT have reciprocal dates?
  7. A triangle’s hypotenuse is 13 units. One of the legs is 12.  What is the triangle’s area?
  8. A history/culture trivia BT: Name a) the man and b) the woman who has/have appeared on the cover or TIME most often. (I mean, what is Google for, right?)
  9. My double exceeds my half by 2. Who am I?
  10. Find three consecutive integers whose sum (adition) equals their product (multiplication).
  11. Is it possible for a year to have two consecutive months with a Friday the 13th?
  12. True or false?  An 8″ (radius) circular pizza has over twice as much pizza as a 6″ pizza of the same thickness.  (Partial credit for correct answer [only].  Full credit for explanation.)
  13. (Repeat?) Can you find FIVE consecutive integers, none of which are prime? (Multiple answers possible?)
  14. If you draw a card from a ‘normal’ 52-card deck (no jokers), what’s the probability that the card you draw will be EITHER a heart OR a king?

Determine the value for “?” in the equations on the left. (Easier than it might look.)

 

 

16. Did you see the GARFIELD cartoon (see 10/24 at link) shared recently (today, for some of you) ?  For an easy almost-freebie, how could the wish of the kid on TV have backfired on him? (multiple answers possible again?)

VIRAL PUZZLE #mathpuzzle #viral #quiz17. Possible multiple answers? (Supporting your answer helps.)

18.

Bonus #1:  How many states’ names can you string together so that the last letter of one becomes the first letter of the next?  E.g., WyominG, GeorgiA,  AlaskA, , . . . etc.  (We’ll keep ongoing records here and everyone who sets, breaks, or ties a current record in a new way will be listed later.)

Bonus #2:  See #10 above.  There are actually THREE sets of triplets that satisfy this condition.  Can you find the other two?

Bonus #3:  See #13 above.  What’s the largest such string (of non-prime [composite]) integers you can find?  (The focus here is on YOU.  Multiple correct answers possible.)

Bonus #4:  See #17 above.  What other attritbute(s) does/do the 3 numbers there share?  (Guess what?  Multiple answers possible.)