NOTE: Newest BTs in red, Bonuses in blue, comments in green, updates in purple.
- Mary’s mother had three daughters. The first two were named April and May. What was the name of the third daughter?
- A cheetah was clocked running 550 feet in 10 seconds. About how many miles per hour is that?
- Find a three-digit perfect square whose last two digits are its square root.
- Ninety-six is 37.5% of what number?
- What is a) the mean and b) the median of the first 10 prime numbers?
- Two dates are called ‘reciprocal dates’ if, when written as fractions, each is the other’s reciprocal. E.g., October 6 (10/6) and June 10 (6/10) are reciprocal dates. Not all dates have reciprocal dates (Sep 21, e.g.), and 12 days are their own reciprocal dates. (6/6, e.g.) In any given non-leap year how many days do NOT have reciprocal dates?
- A triangle’s hypotenuse is 13 units. One of the legs is 12. What is the triangle’s area?
- A history/culture trivia BT: Name a) the man and b) the woman who has/have appeared on the cover or TIME most often. (I mean, what is Google for, right?)
- My double exceeds my half by 2. Who am I?
- Find three consecutive integers whose sum (adition) equals their product (multiplication).
- Is it possible for a year to have two consecutive months with a Friday the 13th?
- True or false? An 8″ (radius) circular pizza has over twice as much pizza as a 6″ pizza of the same thickness. (Partial credit for correct answer [only]. Full credit for explanation.)
- (Repeat?) Can you find FIVE consecutive integers, none of which are prime? (Multiple answers possible?)
- If you draw a card from a ‘normal’ 52-card deck (no jokers), what’s the probability that the card you draw will be EITHER a heart OR a king?
Determine the value for “?” in the equations on the left. (Easier than it might look.)
16. Did you see the GARFIELD cartoon (see 10/24 at link) shared recently (today, for some of you) ? For an easy almost-freebie, how could the wish of the kid on TV have backfired on him? (multiple answers possible again?)
17. Possible multiple answers? (Supporting your answer helps.)
18. 
Bonus #1: How many states’ names can you string together so that the last letter of one becomes the first letter of the next? E.g., WyominG, GeorgiA, AlaskA, , . . . etc. (We’ll keep ongoing records here and everyone who sets, breaks, or ties a current record in a new way will be listed later.)
Bonus #2: See #10 above. There are actually THREE sets of triplets that satisfy this condition. Can you find the other two?
Bonus #3: See #13 above. What’s the largest such string (of non-prime [composite]) integers you can find? (The focus here is on YOU. Multiple correct answers possible.)
Bonus #4: See #17 above. What other attritbute(s) does/do the 3 numbers there share? (Guess what? Multiple answers possible.)
Hi Larry, I realize I’m late getting these submitted and will certainly understand if they aren’t in time for your next blog. I will be curious to see which ones I got correct.
1) Mary
2) 37.5 miles/hr.
3) 625
4) 256
5) a] mean = 12.9
b] median = 12
6) 221 days
7) 30 sq. units
8) man – Richard Nixon
woman – Hillary Clinton
9) 1 1/3 (one and one third)
10) 1, 2, and 3
11) yes, if the 13th falls on Friday in February, it will also fall on Friday in March (in a NON-leap year)
12) If the 6″ refers to the radius on the smaller pizza then FALSE, the 8″ size has an area of 64 pi sq. in. and the 6″ size has an area of 36 pi sq. in. which is NOT twice as much (approximately 1.777).
13) 24 – 28, 32 – 36, 48 – 52, 54 – 58, 62 – 66, 74 – 78, and 90 – 96 are the strings less than 100
14) 17/52
15) bottle = 10, burger = 5, mug = 1, so ? = 16
Bonus #1) I found 2 strings of 12 states: Washington, New Mexico, Ohio, Oregon, New York, Kansas, South Dakota, Alabama, Arkansas, South Carolina, Alaska, Arizona
AND
Utah, Hawaii, Idaho, Ohio, Oregon, New Mexico, Oklahoma, Arkansas, South Dakota, Alabama, Alaska, Arizona
Bonus #2) In addition to 1, 2, 3 listed on #10 there is -3, -2, -1 & -1, 0, +1
Bonus #3) Without going very far beyond 100, I found a string of 13 consecutive integers which are 114 through 126. I’m sure there would be longer ones the higher in the integers you go.
16) If the genie is bad at math, he may not be able to count down from 9 to 1 (giving 9 more wishes).
17) What jumped out to me right away was the number of intersections formed by the line segments, so ? = 4.
Bonus #3) I found 3 more strings of 13 integers: 774 – 786, 508 – 520, and 840 – 852. I also found a string of 19 consecutive integers: 888 – 906.
Bonus #4) All the numbers are perfect squares
BT#1…Mary
BT#2…37.5 mph
BT#3…625
BT#4…256
BT#5…mean 12.9, median 12
BT#6…221 days do not have reciprocal dates
BT#7…Area is 30
BT#8…Richard Nixon and Hillary Clinton
BT#10…1,2,and 3
BT#11…Yes but only the months of Feb and Mar. Since Feb has 28 days, each date in Feb is the same day of the week as the same date in Mar.
BT#12…FALSE A pizza with a 6″ radius has an area of 36pi and one with an 8″ radius has an area of 64pi which is NOT twice as much.
BT#13…24,25,26,27,28.
BT#14…16/52 or 4/13
BT#15…25
BT#17…8. Since the large figure is made of the other two being overlayed, taking away the one valued as 1 leaves the other which must have a value of 8 in order for the overlaying to have a value of 9 as shown.
BT#18…If this is an addition problem, the missing digit in the top row is 0, the missing digit in the middle row is 9, and the missing digit in the answer is 0.
BONUS#2…The three sets of consecutive integers whose sums are equal to their products are 1,2, and 3; -1,-2,and -3; -1,0,and 1.