well yes, clearly. My point is that the those questions, as written, do not have the necessary information in them to lead to one, and one only, correct answer. For both of them there are plausible and reasonable interpretations for several “correct” answers
The pencil one contains all the info needed and has no room for interpretation.
The real question is why such a disparity of pencil quality that would adequately justify the price difference.
But the real money is in the sharpening.
So it isn’t a math problem at all. It’s an english problem.
Likewise many people have difficulty understanding that if an item is on sale for 20% off the original price, and you have a coupon for 20% off your entire purchase, that’s not the same as a 40% discount.
I’ll take “ART IS ANAL PENCILS” for $200, Alex.
If Engineers, accountants, and physicists all fail to understand this relatively simple algebra word problem after you explain it to them, I have to think that the problem lies in your explanation.
Lots of people have pointed out why initially most people get this wrong, but the actual math to solve it is like 7th grade level. I find it really hard to believe that people who had to excel in math at the college level can’t manage to understand this.
I found this trickier than the original problem but it is still solvable with Wolfram Alpha:
Wolfram finds the number of eggs produced by one hen in a day (x) = 0.666667 and the final answer (y) is 16.
Just about every time a sports based thread pops up someone drops in to tell everyone how sports are stupid. At least with sports we know with certainty that people actually enjoy them. This is a game, like sports, only it’s a game that not many people enjoy. It’s like the 15th time your Grandpa pulls a quarter from your ear.
Well in Australia, way back in those days the coin we would have used was called a shilling. If you got a good deal you might have got tuppence or thripenny bit as change.
Australia made the change to decimal currency on 14th February 1966 and we never have used nickels…
OP here. I think I have gained a little insight.
**TriPolar **said, “… That’s what pops into people’s minds and they don’t think any further through because who cares about John and his pencils anyway?” People that know me well respond this way: they look silently in another direction without saying anything hoping that I will leave soon because “who cares about John and his pencils anyway.”
Several posters have suggested that the math problem is deliberately contrived so as to be misleading. Maybe it is a bit contrived. It doesn’t seem to follow the expected order of statements and questions for most ordinary discussions about pencil purchases. A more normal discussion might be as follows:
ZEKE: How much did you spend for those two pencils?
SUSAN: $1.10.
ZEKE: That one is really pretty. How much did that one cost?
SUSAN: The pretty one cost $1.05.
ZEKE: So I guess the plain one only cost a nickel then, right?
SUSAN: Yes.
[ZEKE AND SUSAN HAVE SEXUAL INTERCOURSE IN THE BACK ROOM]
However, consider the following (somewhat contrived) discussion between Alice, Bob, and Charles, who are partners in a small accounting firm:
ALICE: We’re almost bankrupt. The only cash we have left is $1.10.
BOB: What do we need the most that costs $1.10 or less.
CHARLES: We are out of pencils. We can’t do accounting without pencils.
ALICE: Bob, go to the store and buy some pencils.
[ALICE AND CHARLES HAVE SEXUAL INTERCOURSE IN THE BACK ROOM WHILE WAITING FOR BOB TO COME BACK WITH THE PENCILS]
[LATER] BOB: I’m back.
CHARLES: How many pencils did you buy?
BOB: Two. Check out this one pencil. Its really cool. It’s what they call an artisanal pencil.
CHARLES: Did you bring back any change.
BOB: No. I spent all of our money.
CHARLES: Dammit Bob, how much more did you have to spend just to get that stupid artisanal pencil.
BOB: It only costs one dollar more than the regular pencil. Excuse me, I have to take this call. [BOB EXITS ROOM]
ALICE: Bob is such an idiot. We don’t need fancy pencils. If he had just bought regular pencils we would have 22 pencils now.
So, I guess it would be an unusual situation and non-ordinary conversation that set up this math problem. But it could happen. And I still say that it is not a “trick question.”
In Kahneman’s book Thinking Fast and Slow, the question is “A bat and a ball cost $1.10. The bat costs $1 more than the ball. What does the ball cost?” - so there’s no confusion about artisanal pencils.
“Back down” implies, in plain language, “return to the starting point”. It is redundant to add “the same hill”.’
Well, for the record, I’m an engineer, and I got the correct answer on the first try. I really doubt any engineer would get it wrong. We are trained to approach math problems logically, not casually.
Obsessive or compulsive attention to detail, mild paranoia or excessive nitpicking, inability to let go and enjoy the moment, a generally reductive worldview or over analytical attitude.
Related example, it’s a popular wish to have a photographic memory, but the few individuals who actually come close often report it kind of makes them miserable because they cannot recall something bad without reexperiencing the emotional impact.
This doesn’t make any sense. Even if you assume that the half chicken is an actual dead half chicken, and not a real statistical one (which is stupid, a riddle which relies on common reading errors to encourage you to make a real mistake is fundamentally in a different category than one which has more than one legitimate interpretation) it still explicitly says the half eggs are being laid.
But you didn’t use plain language, you didn’t specify the same hill and you said nothing about returning to the starting point.
Your question can be interpreted in that way but it can also be correctly interpreted in other ways.
The uphill and downhill comments might be thought of as an irrelevant factor just like the old “ton of lead or ton of feathers” and dismissed as such. After all, what effect does uphill or downhill have on an average speed you’ve already recorded?
Your question was far too loosely worded to be in the same category as the pencil one and if you asked it to me in it’s orginal form I wouldn’t even try to solve it. I’d have to ask you for addtional information to be able to answer it precisely.
No, your question fills in the details that the original one leaves out. The original one merely says
That is all it says and it is ambiguous with alternative potentially “correct” answers
Telemark is right. He’s not removing the half chicken, just realizing that x chickens laying x eggs in y days will always take y days regardless of what x you use, so you can simplify it by changing x to 1, but y remains the same.