May/June17 Brain Teasers – SUMMARY
REMINDER: Answers in red. Solvers (submit ted/correct) in blue. (Forgive any omissions.) Comments in green. For further elaboration, feel free to ask!
- Homer’s mother has four children. Three of the children are named Spring, Summer, and Autumn. What is the name of the 4th child? Homer! Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Jennifer Steele.
- A man tossed a baseball 20 feet. It stopped in mid-air, reversed directions and came back to him. How can this be explained? He threw it straight up. Rita Barger, Jim Waterman, Amy Ragsdale, Christine Porter, Anita Dixon, Alexis Avis, Jennifer Steele.
- [An old classic!] A brick weighs 3 pounds plus half (the weight of) a brick. How much does a brick and a half weigh? Nine (9) pounds. Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis
- Find three consecutive odd integers which are all prime. 3,5,7. Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis
- You have a string of 10 consecutive integers. The sum of the first three is 39. What is the sum of the last 3? 60. Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis
- If x#y = x + y +7, then what is the value of (2#3) # (7#0)? 33 Rita Barger, Amy Ragsdale, Anita Dixon
- I have twice as many nickels as dimes. If the value of my nickels is $5.00, what is the value of my dimes? $5. Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Jennifer Steele.
- My neighbor has four daughters and each daughter has exactly one brother. How many children does my neighbor have? Five (5). Rita Barger, Jim Waterman, Amy Ragsdale, Anita Dixon, Alexis Avis, Jennifer Steele.
- What is the largest integer you can square and get an answer less than 3000? 54. Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis
- 1/19 is to 1/17 as what number is to 95? 85 Rita Barger, Amy Ragsdale, Anita Dixon, Alexis Avis
- In the first quarter of a game, the Denver Nuggets missed only 7 of their 25 field goal attempts. What was their scoring percentage for that quarter? 72%. Rita Barger, Amy Ragsdale,, Alexis Avis
- Simplify this expression: (99 – 9) x (99 – 19) x (99 – 29) x . . . x (99 – 199). Zero (0). Rita Barger, Alexis Avis
- In my hand, I have two US coins whose total value is 55 cents, but one of the coins is not a nickel. What are the two coins? A half dollar and a nickel. (One of them is not a nickel.) Rita Barger, Jennifer Steele
- A frog is at the bottom of a 30-foot well. Each day he is able to jump up 5 ft, but during the night, he slides down 3 ft. How many days will it take him to jump out of the well? 14 days. (On the 14th day, he gets out before sliding back down.) Rita Barger, Alexis Avis, Jennifer Steele
- “Brothers and sisters have I none, but this man’s father is my father’s son.” To whom is the speaker referring? He is referring to his son. Alexis Avis
B1. Counterfeit Coin #4 Another new twist of Jan/Feb’s problems. I am now convinced this problem can be solved with up to 27 coins(!). So pick your own number(s) and solve: You know one of them is counterfeit – and that it is slightly heavier than the good coins, and you still have your balance scale. Determine the bad coin, still with only 3 weighings. (A ‘weighing’ consists of coins being placed on both sides.) No solutions submitted again. May or may not continue on to next time. (For details of solutions, ask.)
B2. (see #4 above.) It turns out there is only one solution to #4 above. Why is that? Any other collection of consecutive odd integers contains a multiple of 3. [Note that the 3 in 3,5,7 is multiple of 3, but in this case it’s also prime.] (For further clarification, ask.) Anita Dixon (with partial credit to Jim Waterman.)
B3. (see #6 above.) If x&y = x # (y+7), then what is the value of (2#3) & (7#0)? 33. Rita Barger, Anita Dixon.
B4. (see #9 above.) Suppose we do not insist on an integer in #9 above. How (if any) does that change the answer? Considerably! There is NO such number. [The square root of 3000 is 7.34846 . . . and there are always decimals less than that but larger than anything picked earlier.] Rita Barger, Anita Dixon (with partial credit to Amy Ragsdale.)
Mark Your Calendars Now – Plan to Join Us!!
Here are some very early facts. More details to follow.
WHAT: The Great Book Launch Bash! A fun evening of entertainment and book signing.
WHEN: Friday evening Sep 8 and/or Saturday evening, Sep 9. (Times TBA)
WHERE: Branson, MO (9/8) and Springfield, MO (9/9). (Specific venues TBA)
WHO: The CO-HOSTS are Larry Campbell and Todd Parnell. Both Larry and Todd have new books debuting this summer, and will be available both evenings for signings of books (which may be purchased at the event). [More on Larry and Todd to follow.]
BENEFACTOR: Boys and Girls Clubs of Branson. A great group & a wonderful cause.
FUN FEATURES: * OTHER AUTHORS (and at least one artist) will be present and signing books and prints. HELP BGCO! A percentage from sales from ALL authors/artists will go to Boys and Girls Club of the Ozarks. Get books and help a good cause at the same time. ENTERTAINMENT There will be entertainment throughout the evening. Watch for a SURPRISE or two!! CASH BAR – and perhaps other goodies.
YOU will be invited to attend (and some of you will receive special reserved seating). BE THERE!
CAN YOU HELP US?
We want to make this a fun evening for all (and obviously we want to sign/sell books!), but we ALSO want to help the Boys and Girls Club as much as possible, and these all go together. We will be likely be looking for donations to help minimize logistical expenses and maximize our donation to BGCO! Details to follow, but we could be seeking donations at the DONOR, SPONSOR, and UNDERWRITER levels. Please keep this in mind – you can help, whether you’re able to attend or not.
This post contains an electronic version of Rollin’ Down the River’s appendices, for those who wish quicker access to the links.
APPENDIX 1: RESOURSES & MORE INFORMATION
- In Section 1, p. 24, the footnote mentions a resource used to pattern the ‘quiz’ in that essay. Here is a link to the original book, from National Council of Teachers of Mathematics. It is the best book on the general topic I’ve seen. It is not only readable, but provides a wonderful perspective and things to ponder.
- In the Education in an Information Age essay (Section 3, p. 64), there is a Doonesbury cartoon mentioned. It’s amazing to me how successfully that particular strip captures the essence and perspective of this topic, while simultaneously mixing in humor. It is perhaps my favorite ‘educational topic’ cartoon strip. The link is provided in the piece, but here it is again:
- Notwithstanding the cartoon strip mentioned above, there /was no cartoon strip I know of that matches the sheer volume of excellent-while-humorous educational (and mathematics educational) cartoon strips than Calvin and Hobbes. Again, the humor helps drive home the thought-provoking points. Check out this site for a large collection of samples:
- As to “the answers” to the Poetry/Mathematics quiz at the end of Section 4 (p. 89-92), here is the quick version: All the odd-numbered quotes refer to poets/poetry, while all the even-numbered ones refer to mathematicians/mathematics. For the original version of the article, check out the link below. (This is a long (and perhaps surprisingly ‘academic’) article, but the quiz and answers are given in Appendix B at the end.
- Further/ongoing resources. Preferably, this section can take on an ongoing and growing nature through the author’s website(s). If readers have questions or comments, feel free to use the connections and information detailed in Appendix 2. Resources that grow out of those inquiries and from other places will be added to the list, which can be periodically checked. Feel free to check back often.
APPENDIX 2: FURTHER CONNECTIONS WITH AUTHOR
Larry Campbell currently resides in Branson, MO, and he would be delighted to hear from you. He may be reached at email@example.com or larrycampbell@AfterMathEnterprises.com
To visit Larry’s general AfterMath Enterprises website, go to www.AfterMathEnterprises.com. While at this site, you can also sign up for his (free) (Bi-)Weekly Photo/Sharings, delivered on (sometimes alternate) Monday mornings. These always contain one of his photos from around the world (including his 2016 Missouri River trip), along with other features and “Wild Cards” of multiple varieties, all designed to brighten your Monday mornings – and your week.
To visit Larry’s author website, go to www.LarryNCampbell.com This site will contain other book-related connections (including an ongoing Resources link, mentioned in Appendix 1.)
Larry is available for Book Signing Events and/or presentations on a variety of subjects, and he enjoys doing these events. Topics are varied. Some are similar in nature to those in this book, including a talk on “Interesting and Weird Mathematicians and Stores about Them”. He also speaks on his 2016 River Adventure all the way down the Missouri River (by car) from source to mouth, and has several ‘travelogue’ type presentations, with pictures of his various world travels. For further details, and/or to compare calendars, contact him at the address(es) above.
APPENDIX 3: ASSORTED BRAIN TEASERS
Also known as “Yoga for the Mind”
“Brain Teasers” are wonderful tools for the budding problem solver in mathematics and elsewhere, but they are not For Math Nerds Only! They can be a great deal of fun, as well. Listed below is a sort of “Top Ten” of some Easy-To-State Favorites, after which some links will be provided to others, as well. Lighten Up. Pick (only) the ones you that grab you, and by all means, have fun!
- The Horse Trader
A man buys a horse for $60, sells it for $70, buys it back for $80, and finally sells it for $90. Did the make any money on the transactions, and if so, how much?
Ten people enter a room for a meeting. If they all shake hands with each other (once each), how many total handshakes will there be?
- Dollars and “Sense”
In my hand, I have two common US coins whose total value is 55 cents. One of the coins is not a nickel. What are the coins?
- Calendar Cubes
How are the digits 0 – 9 placed on two cubes to form a calendar (often seen in banks, etc) that can display every date of any given month? (Always use both cubes: 01, 02, 03, . . . 30, 31)
- It’s All “Relative”
“Brothers and sisters have I none, but this man’s father is my father’s son.” To whom is the speaker referring?
- Buckets of Water
You have TWO completely unmarked buckets. One will hold exactly 7 gallons, the other 4 gallons. How can you measure exactly ONE gallon of water? (What if the smaller bucket holds 5 gallons instead?)
- Number Sequence?
What are the next two letters in this sequence? O, T, T, F, F, S, S, ____, ____
- The Frog in the Well
A frog is at the bottom of an empty 30 foot well. Each day he is able to climb up 5 more feet, but at night, he slips back 3 feet. At this rate, how long will it take him to escape the well?
- The “Average” Driver
Ralph drives 60 miles at an average speed of 30 mph, then returns over the same route at an average speed of 60 mph. What was his average speed for the round trip?
- Word Trivia
Consider the spellings of each positive whole number. A) Which number’s spelling is the first to contain the letter A? B) Which number’s spelling is the only one in alphabetical order? C) Which is the only one in reverse alphabetical order?
ANSWERS and More Brain Teasers?
Feel free to share proposed solutions and/or questions with the author, using the links provided in Appendix 2. In order to promote the needed ‘play/think’ time for these, the answers are not immediately given in a link. Contact the author for a link to the answers.
To see an archive of Brain Teasers and answers that have been used in roughly 2 years of Weekly Mailings, visit http://aftermathenterprises.com/various-answers/ There are also other links to more Brain Teasers available by request.
If you want to receive periodic Brain Teasers (followed by answers later), visit the AfterMath website (www.aftermathenterprises.com) and sign up for the Weekly (sometimes Bi-Weekly) Photo Sharing.