Teasing Out Some Math Jokes
March 6, 2013 at 10:55 am
Let’s do a quick warm-up before jumping into this post.
A boy leaves his house headed for school, walking at a rate of 4 miles per hour. Ten minutes later, his sister leaves the school headed for home, walking at a rate of 3 miles per hour. Assuming they travel the same route (just in opposite directions), which one will be nearer the school when they meet?
This problem is based on the first puzzle that appears in Mathematical Teasers by Julio A. Mira. As best I can tell, this book is out of print, and probably for good reason. Written in 1970, it contains no semblance of political correctness. For instance, the image below appears at the beginning of Chapter 1:
Click to Enlarge Image
Hmm… a pigtailed coed in a skirt sitting on a desk, tickling the chin of a math professor? There is no doubt an editor in 2013 would prohibit such an image from appearing in a publication; quite honestly, I’m even surprised an editor allowed it 43 years ago.
My copy of this book was obtained when the National Council of Teachers of Mathematics cleaned out their staff library. Inside the front cover, an insert states that it was a review copy “sent with the compliments of Barnes and Noble, Inc.,” and a stamp on the insert reads:
RECEIVED
MAY 26 1970
NCTM
Despite its political incorrectness and outdated contexts, my five-year-old sons have been enjoying the puzzles in the book. But they aren’t just puzzles. Like the warm-up problem above, they are jokes, in the sense that the punch line (answer) is unexpected. The following are a few of my favorites.
- A man with $50 in a bank account withdraws $20, leaving $30. He then withdraws $15, leaving $15. Then $9, leaving $6. And finally $6, leaving $0. The sum of his withdrawals is 20 + 15 + 9 + 6 = $50, as expected, but the sum of the remainders is 30 + 15 + 6 + 0 = $51. Where did the extra dollar come from?
- If it takes 3 minutes to boil an egg, how long will take to boil a dozen eggs?
- How many cubic inches of dirt are in a hole that measures 1 ft. × 1 ft. × 1 ft.?
- A man purchased a pair of shoes that cost $25 and gave the shop owner a $100 bill. After the man left with the shoes and his change, the owner took the $100 bill to the bank, where he was told that it was counterfeit. What was the total loss to the owner?
- Every day, Johnson’s cat would climb 11 feet higher in a tree that is 63 feet tall. But every night, the cat would climb back down 7 feet. How many days would it take her to reach the top of the tree?
No answers will be posted. Y’all can attempt to reach consensus in the Comments section.
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Entry filed under: Uncategorized. Tags: bank, cat, change, coed, counterfeit, dirt, egg, Julio A. Mira, NCTM, shoes, teasers, tree.
1.
xander | March 6, 2013 at 11:39 am
Warm-up: When they meet, the sister will be closer to the school. By about 6 inches.
(1) Boo! Someone is trying to be clever.
(2) 10 Minutes. I can only fit 4 eggs in my little pot at a time, so 3 minutes times 3 batches, plus a minute (or maybe two) to swap the eggs around. Of course, I probably wouldn’t want to eat a 3 minute egg—I don’t like the idea of contracting salmonella.
(3) I don’t know—what is the hole full of?
(4) Zilch. That’s what insurance is for, amirite?
(5) I’m afraid that I don’t get this one.
Aside from no knowing where the cat started, I think that I am missing something obvious.
xander
2.
venneblock | March 6, 2013 at 1:16 pm
Does it help to know that the cat started at the bottom, 0 feet? First day he climbed up 11, down 7 that night, so he’s at 4 feet at start of Day 2; and so on.
3.
xander | March 7, 2013 at 11:26 am
Even so, where’s the joke? Or is it really just a straightforward problem?
xander
4.
venneblock | March 8, 2013 at 8:15 am
The term “joke” is subjective, as is the term “straightforward.” My five-year-old sons didn’t find this one straightforward at all; it didn’t help that my Yale-educated wife led them down the wrong path. (In her defense, she studied forestry, not math, and she is far better at wielding a chainsaw than a calculator.) So for you, the problem was simple, but my guess is that 50% or more of potential solvers would fall into the typical trap. As for it being a joke, well, it’s not really a joke, just that there’s a slight twist to the problem.