May/June ’21 Brain Teasers

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 2^nd 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. 
8. If p is an odd prime, find the sum of all the factors of 4p. 
9. SIMPLIFY:  7/22 ÷ 14/44
10. 
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]