NOTE: Newest BTs in red, Bonuses in blue, comments in green, updates in purple.
- What kind of cheese is made backwards? 🙂
- What word begins and ends with ‘e’, but only has one letter?
- 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. 🙂 ).
- 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)?
- How many spherical meatballs of radius 1 can you make from a spherical meatball of radius 3?
- (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?
- I am < 25. My ones digit is twice my tens digit and the digits add to an even number. What am I?
Find the area of the shaded region to the right. –>- 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?
- 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?
- I am an odd integer. If you take away one letter from my name, I become even. What am I?
- When is it possible to subtract 1 from 19 and get 20? When is half of 13 = 8?
- How many prime factors does 2020 have, and what are they?
- How many two-digit integers are divisible by either 3 or 5?
- Find 14232 – 14182. (You can probably crank this out fairly easily [?], but there’s a clever way to do it very quickly.)
- 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? 🙂 ).
BT#1…Edam
BT#3…There are eight: 1243,1342,2134,2431,3124,3421,4213,4312.
BT#4…Rounding up because there are no fractions of cents (unless dealing in the Stock Market) one would have to spend $3,422,313.49 per day in order to spend a trillion dollars by their 80th birthday
2. Envelope
3. 1243/11 = 113
2431/11 = 221
2134/11 = 194
3421/11 = 311
3124/11 = 284
4213/11 = 383
4. $34,223,134 and 84 cents
29,220 days in 80 years
60 regular years with 365
days = 21,900 days
20 leap years with 366 days
= 7,320 days
1 Trillion/29,220 = 34,223,134.84
5. The answer is 27 meatballs
The volume of a sphere is 3/4 pi r3
R = 3: 3/4 pi 3 cubed = 113.09724
R = 1: 3/4 pi 1 cubed = 4.188786
113.09724/4.188786 = 27.000004
Bonus 1: The answer is 9
Sum. # Combos = Sum
1. 1
2. 1
3 2
4. 3
5. 5
6. 5
7. 7
8. 7
9. 9
10. 8
11. 8
12. 6
13. 6
14 4
15. 4
16. 2
17. 2
Checking the math,as suggested,BT#4 should be $$34,223,134.84 per day.
BT#6…C=55
BT#7…I am 24.
BT#8…Area is 400cm – 100pi.
Bonus 2…x squared – pi rsquared.
Typo: Answer to BT8 should read 400 cm Squared…
I am SO far behind on these. But here goes with the ones I think I have figured out. My hubby helped me with the first two.
1. Edam
2. Envelope–usually just one letter in it.
3. I found several. Of course I had to Google the rule to get some help. 1243, 1342, 2431, 2134, 3124, 3421, 4213, and 4312. There might be more, but my brain is teased enough right now!! Is there a formula for this or just guessing a lot like I did?
4. That newborn and his parents are going to be VERY busy spending a bit under $34,250,000 a day. I wondered how many leap days there are in his/her 80 years. If you add in 20 leap days, the amount is a bit over $34,223,000 a day. WOW!
5. About 27 or 28 meatballs with a radius of 1 from a meatball with a radius of 3. Can that be right? Another WOW!
6. I know there has to be a formula for this one, but my brain is way too old to remember the formula. I did a bit of guesstimating and found C to be 55.
7. I got 24 for this one.
8. The area of the shaded area is 86 square centimeters. For the bonus, would it be (x squared) – (3.14 [x/2]squared) = Shaded area, y cm squared. (Area of the square minus the area of the circle.) I don’t know how to type that as a proper expression. I tried.
I have NO idea f
or Bonus #1 unless the answer is 11, but that is sort of thinking of probabilities, or at least probables.
BT#9…For any three consecutive integers,A,B,and C, the product AC plus 1 is equal to the square of B.
BT#10…If she stops after writing 630 digits, the last integer written will be 7 (as in 347).
3. 1243, 1342,2134, 2431, 3124, 3421, 4213, and 4312 are all divisible by 11.
9.The square of the middle number will always be 1 greater than the product of the other two.
If the numbers are n, n+1, and n+2:
(n+1)^2 = n^2 + 2n + 1
n(n+2) = n^2 +2n
#2: envelope
BT311…I am number 7.
BT#12…when nineteen is a negative quantity.
BT#13…2020 has just one prime factor, the number 5.
1) Edam cheese
2) envelope
3) yes, there are 8 arrangements which are divisible by 11: 1243, 1342, 2134, 2431, 3124, 3421, 4213, and 4312
4) $34,223,134.84 each day (allowing for 20 leap years)
5) either 26 or 27 small meatballs (depending on rounding and what version of pi you use)
6) C = 55
7) 24
8) 400 – 100pi or approx. 85.841 sq. cm
9) The middle number squared is always one more than the product of the other two
10) 276
11) 7 – seven take away the s leaves even
12) A- when you are subtracting negative one (-1)
B- still thinking on this one
13) 3 prime factors of 2020: 2 (squared), 5, and 101
BONUS 1) most likely sum is 9 (8 ways to make it)
BONUS 2) x^2 – (x^2/4) x pi (This is hard to express without the ability to write fractions.)
BONUS 3) I started out trying to make a Venn diagram, but I kept getting confused. (I assumed the words “cards” should have been “cars.”) Not sure if I will keep trying on this.
BONUS 4) 34/99
BONUS 5) let x = 1st integer, x + 1 = 2nd integer, and x + 2 = 3rd integer
product of 1st & 3rd integers = x(x + 2) or x^2 + 2x
middle integer squared = (x + 1)^2 or x^2 + 2x + 1
BONUS 6) 12 total factors of 2020: 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, and 2020 (I can “see” many of these from combinations of the prime factors found in #13.)
BT#2…The word envelope.
BT#14…..There are 30 two digit numbers that are multiples of 3 and there are 18 that are multiples of 5, but when you subtract the 6 that are multiples of both 3 AND 5, you are left with the 42 that are multiples of 3 OR 5.
BT#15…14205
BT#16…The decimal.000…01 with an infinite number of zeroes between the decimal point and the one would be as near to ZERO as possible. However those zeroes are neither positive or negative. So the 1 at the end of the decimal is the closest positive number to the ZERO no matter how many zeroes precede it in the decimal.
Bonus #11…The most common total of any 2 of the 10 balls is 11.
Bonus#3…There are 8 sports cars that are neither red nor blue.
Bonus#6…The number 2020 has 12 factors: 1,2,4,5,10,20,101,202,404,
505,1010,and 2020.
14) total of 48 (30+18)
15) 14,205 (can be found using difference of squares -> 2841 x 5)
16) unless this is a trick question, the smallest positive number doesn’t exist because between any 2 real numbers there is another real number (ie. numbers are densely ordered)