Brain Teasers – May/June ’20

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

1. What kind of cheese is made backwards? 🙂
2. What word begins and ends with ‘e’, but only has one letter?
3. The integer 1234 is not divisible by 11. By re-arranging the digits, can you find one or more integers that are divisible by 11?  (A yes/no answer does not get full credit. 🙂 ).
4. A new-born infant was given 1 trillion dollars at birth.  (Wow!).  How much would he/she have to spend (average) each day to use all the money in 80 years (assuming no interest accrued)?
5. How many spherical meatballs of radius 1 can you make from a spherical meatball of radius 3?
6. (Repeat) The sum of A & B is 112.  A is 4 more than C, and B is 2 less than C.  What does C equal?
7. I am < 25.  My ones digit is twice my tens digit and the digits add to an even number.  What am I?
8. Find the area of the shaded region to the right.  –>
9. Take any 3 consecutive integers.  Square the middle one and multiply the outer two together.  Try this several times and see what you notice.  Can you formulate a rule?
10. Peggy is writing down the integers from 1 to 1000. (Who knows?) She stops to rest after writing 630 digits. What is the last integer she wrote?
11. I am an odd integer.  If you take away one letter from my name, I become even.  What am I?
12. When is it possible to subtract 1 from 19 and get 20?  When is half of 13 = 8?
13. How many prime factors does 2020 have, and what are they?
14. How many two-digit integers are divisible by either 3 or 5?
15. Find 1423² – 1418².  (You can probably crank this out fairly easily [?], but there’s a clever way to do it very quickly.)
16. What is the closest positive number (not just integer) to 0?

 
BONUS 1:  Ten ping-pong balls are numbered from 1 to 10.  If two balls are drawn at random, what is the most likely sum of the numbers on the balls? (this can be done with knowing any probability.)
BONUS 2:  See #8 above. Re-label the 20 cm distance to a more general x cm.  Find an expression for the area of the shaded region.
BONUS 3:  Every red card at an auto show was a sports car.  Half of all blue cards were sports cars.  Half of all sports cars were red.  There were 44 blue cars and 30 red cars.  How many sports cars were neither red nor blue.
BONUS 4:  Can you find a ‘fraction’ (one integer/another) whose decimal equivalent is the (ever-repeating) .3434343434  . . . ?
BONUS 5:  See #9 above.  If you have conjectured a ‘rule’ here, can you prove it?
BONUS 6:  See #13 above.  How many total factors does 2020 have?  (and what are they?  That’s not a trivial question.  There’s actually a way to know how many w/out figuring them and counting directly.  Isn’t math wonderful? 🙂 ).