Larry Campbell Brain Teasers

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 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]

6 thoughts on “May/June ’21 Brain Teasers”

  1. BT2…a clock. But if it had arms and legs would it then be a grandfather clock? All the grandfathers I know have them.
    BT3…True. The reciprocals add up to 2 1/4.
    BT4…second place.
    BT5…1/12.
    BT7…4 1/6.

  2. BT6…3x+3
    BT9…1
    BT10…bookkeeper
    BT11…contains all 5 vowels one time. “facetiously” includes the “y”.
    BT12…ratio of 1:4

  3. 1. 1 is not a prime. 7/5/32
    2. A clock or a watch
    3. False. Factors of 4 are 1, 2, 4. Reciprocals are 1/1 + 1/2 + 1/4 = 1 3/4 < 2.
    5. 3/4
    6. 3x + 3
    7. D. 10
    9. 7/22/ 14/44 = 14/44/ 14/44 = 1
    10. bookkeeper, bookkeeping, Woolloomooloo, Australia
    11. The vowels are in alphabetical order. Facetiously has all of the vowels in alphabetical order.
    12. Pi r sq. Pi 1 sq: Pi 2 sq = 1:4.
    B2. The largest cube is one that goes through with a face with a diagonal of 8. The sides are 2 a squared = 8 sq – sort of 32 or approximately 5.656854. Another orientation of the cube moving through the circle is on the cube’s diagonal with the diagonal = 8. 8 X sort 3 = 4.6188. So, sending the cube face first is the largest.
    B3. 3x + 2 and 3x + 4.

  4. Not sure where I left off last time.
    #10. Bookkeeper
    #11. All vowels are used in alphabetical order
    #12. 1 to 4 ratio of smaller to the larger
    #14. If there are an even number of neg. integers, multiplying gives larger answer
    With odd number of neg integers the sum is larger
    Will send others if I get there.

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