SUMMARY: Solutions & Solvers – May/June 21

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 2^nd 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. 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