NOTE: Newest BTs in red, Bonuses in blue, comments in green, updates in purple.
- What is the value of this fraction? (6 – 9 x 7) / (6 + 4 x 3)
- A palindrome is a number that reads the same forwards and backwards. How many palindromes are there between 1 & 100?
- A group of teenagers went into a fast-food restaurant. They each bought exactly the same thing and their total bill was $44.11. How many were in the group?
- How many whole numbers are between the square roots of 8 and 80?
- (Repeat?) The average score of 6 tests is 93 (on a scale of 0 – 100). What is the lowest possible grade on any one test?
- The sides of a triangle are 8, 15, and 17 units. If each side is doubled, what is the area of the new triangle?
- (Repeat) Consider the spellings of the counting numbers. A) What number is the first to contain the letter ‘a’? B) What is the only number to be spelled in alphabetical order? C) Same as B, but reverse alphabetical order?
- (Repeat) The 22nd and 24th Presidents of the US had the same mother and father, but were not brothers? How can this be?
- (Semi-Repeat) Can there ever be two consecutive months with a Friday the 13th? (Why?)
- The Feb 10 Mailing mentions Year Product Days (See Wild Cards or Item 4 of this link.) As mentioned, 2018 has (exactly) 5 of these special dates. A) What are the 5 YPDs this year? B) Is this the FIRST year this century with (exactly) 5? C) 2012 had 6 YPDs. Have there been others since then?
- There are five (5) sisters on the main floor of the house, and they are the only ones home.. Ann is reading, Margaret is cooking, Katy is playing chess, and Marie is doing laundry. What is the fifth sister doing?
- I simply don’t believe the “95%”. I’ll bet many of you can get it!
BONUS 1: Refer to the humorous ‘proof’ that all numbers are interesting. The technique used there won’t work in the infinite case (no ‘smallest’ number necessarily!) Can you think of a similar approach to the ‘proof’ that would work?
BONUS 2: Refer to #2 above. How many palindromes are there between 100 and 1000?
BONUS 3: Refer to #10 above. Are there any YPDs in any century with seven (7) or more YPDs?
BONUS 4:
6. 240 square units
BT#1…-3 1/6
#2…If a palindromic number must contain at least two digits, then there are 9 of them. If not, there would be 8 more, a total of 17 between 1 and 100.
#3…11 teenagers spent $4.01 each.
#4…Six whole numbers, 3 through 8.
#5…the lowest possible score on any of the 6 tests would be 58.
#6…The area of the original triangle is 60 units. When the sides are doubled, the area of the new triangle is 4 times the area of the first triangle, 240 units.
7C..Reverse order, ONE
8…They were the same person, Grover Cleveland.
9…Friday the 13th can exist in both February and March of any non-leap year because Feb has 28 (multiple of 7) days.
11…Sister # is playing chess with sister Katy.
12…There are 30 balls.
#11 should be sister #5 is playing chess with Katy.
1) -19/6 or -3 1/6
2) 9 palindromes (multiples of 11)
3) 11 teenagers (only # that divides evenly)
4) 6 whole numbers
5) lowest possible score: 58
6) A = 240 units squared
7) A) 1,000 (one thousand)
8) He was the same person, Grover Cleveland
9) Yes, in a NON-leap year, if Feb. 13th falls on Friday, March 13th will also be on Friday
10) A) 1/20/20, 2/10/20, 4/5/20, 5/4/20, 10/2/20
11) playing chess with Katy
12) my guess: 22 balls (16 seen in picture + 6 more not seen on the back side)
I have been overwhelmingly busy for the last month so I’m getting this submitted late. I hope it’s still in time to be “counted!”