Sadistic math problems
Bookworm on Feb 14 2007 at 7:31 pm | Filed under: Education
Am I the only one who thinks the double negative in this Houghton-Mifflin math problem renders it almost unintelligible?
74 apples are placed in small bags. Each bag holds 5 applies. How many apples are not placed in the bag that is not full?
Pardon me for asking, but what the heck does that mean? I know solving this problem reveals that you have 14 full bags, and 4 apples remaining. Presumably, the befuddled textbook authors want the child to conclude that the last bag is one apple less than full, but they’ve actually asked an impossibility? Think about it: the question as phrased refers to nonexistent apples, because aside from the four remaining apples actually placed in the bag that is incompletely filled, there are no remaining apples that haven’t been placed in the bag that is not filled. If there were a remaining apple, the bag would be full.
Gibberish, pure gibberish, and my hard-working, intelligent, and logical daughter inevitably got this illogical question wrong.
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So what is the problem? The correct answer is 70. 4 of the apples were placed in the bag that is not full. 70 of the apples were not placed in the bag that is not full. ;)Who vets these things anyway?
Yours would be the correct answer, DQ, were it not for the fact that the worksheet is labeled “Problem-Solving Skill : Interpreting Remainders.” Here, they seem to be asking about hypothetical applies, rather than real ones, whether the 70 that don’t fit into that partially filled bag or the 4 that do!
The answer, of course, is an unknown, but very large number: the total number of apples in the world minus four.
P.S. I agree, the question is nonsensical.
Here’s one that’s even more sadistic. A math teacher, whose name I don’t know, claimed he could make up a test which 6- or 7-year-olds could pass, but adults would certainly flunk. Here’s a sample question:
What is the next letter in this series:
O T T F F S S E N
Don’t spend a lot of time on it. If you haven’t solved it in two minutes, you never will. Give it to your 7-year-old daughter.
Nobel Laureate Irving Langmuir spent a whole day working on it. When told the answer, he was so mad he almost fired the physicist who gave it to him.
Answer tomorrow night for those of you who don’t have access to a kid .
If, indeed, they are asking about hypothetical apples, not just the 74 real apples in the problem, I agree with Highlander. The sequence in #4 is easy, but I won’t give it away. Hint: here’s a closely related sequence with a different next letter — T T T F F S S E N
Good for you, DQ! Clearly you got it!
BW,
This one belongs to DQ. In proper English, double negatives are improper. The purpose of English is to communicate with the least misunderstanding.
In math, double negatives occur all the time. The negative of a negative is a positive. The problem you mention is completely self contained. In the universe of 74 apples, 70 are in full bags, and 4 are in a partially filled bag.
As far as viewing the wording of the problem strange, remember that Lewis Carroll was a mathematician. My sister is one also, and she is definitely from the other side of the looking glass.
Al
I’ve had the opportunity to hear “from the horse’s mouth” the smug, hermetically sealed rationale for this sort of question. The experience was not pleasant.
You and DQ would both be write Al, were it not for the fact (a) that the problem is about remainders (and 4 is the remainder when you divide 74 by 5) and (b) the teacher wrote that the correct answer is 1.
Greg: What do you mean?
As I recall, the rationale for that sort of question has to do with a purposeful obfuscation and a selection for kids who can see through the fog, which is to say that – ipso facto – your otherwise brilliant student, Book, didn’t measure up to the snuff that the question’s designers were looking for.
1? has that teacher been reading too many math texts lately?
The correrct answer is 1? On which planet? Evidently the teacher couldn’t make it through the fog, either.
FWIW, I view the “apples” problem as fairly straightforward; but I be stumped on the alphabet series thingy that Highlander posed. No bambinos around here.
I get either 70 or “all apples in existence minus 4″ as listed above. If the desired answer is “1″ then the proper phrasing would be “how many apples would you need to make the last bag full” or something equivalent.
There’s really no excuse for this kind of sloppy writing. But having worked for a textbook publisher and knowing some textbook writers, it’s way too common. There’s a tremendous pressure to “update” the books (which usually means a new cover and new interior art), bizarre restrictions on the language you can use, and everything is always being done in a tearing hurry at the last minute.
I wouldn’t have been able to get the right answer on the apples question, but I knew the answer to the letter sequence thing almost instantly. I’m 61. Does that mean I’m in close touch with my inner child? (I’ll keep the secret.)
DQ and judyrose …
The good news is you got the answer, which means you are good at thinking outside the box. The bad news is you’ll probably never win a Noble Prize in Physics.
Congratulations!
Re #10: You can retrofit it as much as you want, but ambiguity is always a product of poor thinking, and can never be justified as an excuse for demanding something from the poor reader. But since your writing often demonstrates that ambiguity is your home country, perhaps you do articulate one motive behind it. That is, if you, as the writer, don’t know how to think well, you can use ambiguity to force the task of analysis onto your readers. Just don’t be surprised if they come up with answers other than you expected or were hoping for.
And yes, this is more of a personal attack than you’ll usually find me voicing at my blog but, quite frankly, I’m tired of the unreasoning animus you continuously turn on me.
BW, Greg is worthy of about as much respect as a horse’s hind end, but I’m glad you came back at him. As the recipient of perhaps his most insulting volley (Comment No. 18, What is Racism?, posted by DQ, Jan. 2nd), I applaud you and agree wholeheartedly with your remarks. Since the purpose of language is to convey meaning, those who choose instead to obscure meaning have not joined the discussion in good faith. (Granted, some people are better at writing clearly than others, but I’m talking about people who play games with words just to get under your skin.)
You asked for a clarification [9], Bookworm, and I offered what I recalled from having heard a presentation the subject of testing to identify the exceptional student [10]. Apparently, obfuscation is one approach. It’s not the approach I’d adopt — basically for the reasons you outline, but also for the reason that I indicated above — that, in fact, there is every reason to think that the exceptional student is as baffled by unclear language as the rest of us.
I am worried, because I thought that 1 was the answer they were seeking.
I confess that when I first read the problem, I uttered an expletive and moved on. After reading the comments, I went back and struggled through it. (Actually, I thought the logical answer should be 4, but decided that did not fit the phrasing.) Unlike Highlander, I defined the universe as the capacity of the bags. Of course I was lousy in math.
I wait with bated breath for the answer to the sequence. I have an answer, but I am not confident.
Here’s the answer as promised:
The next letter is “T”.
To see why, count the letters:
“O”ne “T”wo “T”hree “F”our “F”ive “S”ix “S”even “E”ight “N”ine “T”en
Those of you who got it: congratulations! Those of you who didn’t: console yourselves that neither did a Nobel Laureate after a whole day working on it.
The answer was 1 ???? !!!
Time to find a new math teacher.
I got highlander’s sequence in short order, but I am dismayed that I still haven’t solved DQ’s.
Could I have the answer, please?
Al
Congratulations Al. I think DQ’s is:
“T”en “T”wenty “T”hirty “F”orty “F”ifty “S”ixty, etc.
hilarious. One? Haha.
Hi Al,
Highlander’s got it. The interesting question is whether the next in sequence after “N”inty is O, H or maybe OH for One Hundred. DQ
The question is puzzling, and I think it’s a typo in the math book, so I wouldn’t even answer it (or have my child answer it). Or I would cross it out, rephrase it to make more sense, then have my child answer it. If my kid thought she’d get in trouble with that, I’d write a note to the teacher about it for her to take in with her math homework. I’d like to hear the teacher explain that problem if it’s NOT a typo.
Hi DQ and highlander,
Thanks much. The issue is where you put the decimal point.
(always a vexing problem)
As far as going beyond “One Hundred”, you could also consider
logrithims(spelling?) That would really confuse 99.9999% of the populace. Since we have hand held calculators, few know what logs are. Just ask Issac Asimov.
Gee, I just had a thought. Do you think little Book’s math
teacher knows what logs are/where? Doubt it.
Al