NOTE: Newest BTs in red, Bonuses in blue, comments in green, updates in purple.
- 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?
- What has a face and two hands, but no arms or legs?
- True or False? The sum of the reciprocals of the factors of 4 is greater than 2.
- You are running a marathon and overtake the person in 2nd What place are you in now?
- One-fourth is one-third of what number?
- If 3x + 1 is an even number, what is the next larger even number?
- If p is an odd prime, find the sum of all the factors of 4p.
- SIMPLIFY: 7/22 ÷ 14/44
- More English oddities: ‘FACETIOUS’ is the only word in English which has this property. Can you spot it (the property)?
- 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?
- Suppose John’s average heart rate is 72 beats/minute. Given that, how many times would his heart beat in a day?
- Pick ANY 6 negative integers. Which is bigger – their sum or their product, or might it vary?
- 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]
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.
BT6…3x+3
BT9…1
BT10…bookkeeper
BT11…contains all 5 vowels one time. “facetiously” includes the “y”.
BT12…ratio of 1:4
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.
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.
#15. 1/4 x 2 to the 40th equals 2 to the 38th
#5. 3/4
#7. B
#9. 1