NOTE: Newest BTs in red, Bonuses in blue, comments in green, updates in purple.
- I recently cleaned out my MSU ‘Emeritus’ office (whew!). I found two items tacked to a bulletin board. One was Hampton’s Travel Tips #628. The other was a coupon for a drawing, and was numbered 9998896. Knowing my fascination with numbers, why might I have saved each of these? (LOTS of possible answers here, of course, and most will receive credit.)
- Perhaps you’ll remember KrazyPic1 from Aug 26. Assuming all 4 ‘highlighted’ digits there are used once-each in a 4-number code, how many possible codes are possible?
- Name two consecutive primes numbers whose product is 899.
- What starts today, can’t be found at noon, and is required to end sunset?
- Melissa went to dinner with Andrew, George, and Ulysses. She ate along, but they all showed up to pay for the meal. Why?
- Which number is the third smallest of these? 0.3, 3.03, 0.303, 3.3303, 3.303
- Find the sum of the digits of the largest even 5-digit number that is not changed when its ones and ten-thousands digits are interchanged.
- If there are four cars ahead of a car, four cars behind a car, and a car in the middle, what is the fewest number of cars in the line?
- (Is this a repeat?) What three letters can be arranged to describe a beverage, a verb, and a homonym? (Perhaps that should read homophone?)
- 1/5 ÷ 1/5 ÷ 1/5 ÷ 1/5 = ?
- Find a palindrome that is a cubic number less than 2000.
- How can you plant ten seeds in eight rows with three seeds in each row?
- (Repeat) Using each of the ten digits once, find two five-digit numbers with the greatest possible product.
- (Repeat) What’s a good method to quickly solve this problem mentally? (2019 + 2019) x 50
- (Repeat) What part of a half square foot is a half foot square?
- (Repeat) How many cards must you draw from a deck of 52 cards to be sure that at least two are from the same suit?
BONUS 1: We’ve done several variations of the billiard ball/counterfeit coin problem recently. Here’s a most interesting new one (at least to me): You have the usual 12 counterfeit coins, and now you know that TWO of them are counterfeit and are too heavy (but both ‘bad’ coins weigh the same.). Can you determine/identify BOTH the bad coins in five (or less) weighings with the same balance scale?
BONUS 2: For real math nerds! 🙂 How many pairs of integers p and q exist such that (p^2+1)/q and
(q^2+1)/p are both integers? (Shared by Don Hayes, who says he saw it in a movie.)
BONUS 3: Arrange the integers from 1 – 16 in such a way that the sum of any two consecutive integers is also a square.
BONUS 4: See #12 above. The source I used for this problem says “ten seeds in ten rows”. I’m not sure I believe it?! (I can get 8 rows, so I changed wording, but . . .). Can anyone help out?
CREATIVITY BONUS A: (I was certain this would attract some attention! 🙁 C’mon folks – I know we have some creative and/or smart-alek-type folks out there!!) The Herman cartoon below has had the caption (temporarily) removed. Submit your own caption and get us laughing!! (Later we may decide we like some of these submissions better than the original!)
CREATIVITY BONUS B: Submit a good Creativity Bonus idea for this section!!
BT #3: 29 & 31.
BT #4: The letter t.
Bonus 1: Yes. The procedure is quite long, but start out by dividing the coins into 4 groups of 3 coins each. I can describe the entire method by mail, if you wish.
Bonus 2: I also submitted this problem.
#4…The letter T.
#8…Five cars. The red herring is that the word “car” in the clues refers to the same vehicle. Not so.
#9…tea, eat, and ate.
Bonus 3: 16,9,7,2,14,11,5,4,12,13,3,6,10,15,1,8
#9 tea,eat,ate.
Here are a few more triplets:
arm,mar,ram
are,ear,era
art,rat,tar
11. 1331
#5…Andrew. George, and Ulysses are images on paper money.
#6…Third smallest is 3.03
#7…Largest even 5-digit number whose ones and ten thousands digits are interchangeable is 89998 whose digit sum to 43.
#10…25
2) 4! = 24 possible codes
3) 29 x 31 = 899
4) the letter T
5) They were pictured on the bills she used to pay for her meal ($50, $20, and $1 bills) [Note: I was assuming the word “along” should have been “alone” in the problem.]
6) third smallest is 3.03
7) sum of digits = 43 for the number 98998
8) 5 cars
9) beverage – TEA, verb – EAT, homonym – ATE (The 3 letters are A, E, and T)
10) 25
11) 1331 is 11 cubed (intentionally problem #11?)
13) 97530 x 86421 =
8,428,640,130 (just a guess with a little guess and check)
14) Convert the quantity in () to 2019 x 2, then use the associative property to multiply 2 x 50 first and then use the “shortcut” to add 2 zeros after 2019 to get the answer 201900
15) ??? The wording is really messing with my brain on this one!
Bonus 2: I found 7 pairs of numbers: p=1 & q=1 / p=1 & q=2 / p=2 & q=1 / p=-1 & q=-1 / p=-1 & q=2 / p=1 & q=-2 / p = -1 & q = -2 [or I guess that could be considered 6 pairs of distinct integers?]
Bonus 3: 8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9, 16