I thought it was easy, especially after seeing the diagram.
I also noticed, at the bottom of the page, that they give a link to “The full rankings of the top countries in science, math, and readgin”. It seems they didn’t test for proofreading.
It took me just a few seconds to figure out how to solve the problem, maybe 2 minutes to actually work out the math on paper.
The factual question was the problem itself. In retrospect, it deserves to be in MPSIMS.
Much like the problem, I wasn’t looking for anything deeper than what was on the surface.
I just thought it was an interesting little problem with an interesting accompanying problem. However now I am curious as to how people intuitively knew that the opening was going to be 1/6 of the circumference so quickly - especially those of you who didn’t use the picture. Just curious to see what your thought processes were.
I was expecting to be embarrassed by a surprisingly difficult problem… how is this supposed to be remotely challenging, even for a high schooler? The diagram should make it immediately obvious that the solid portions must cover the arc between two wings, which is a third of the full circle for each, so the two doors can cover the remaining third. If the only thing you remember from math class is the most elementary fact about circles, you can get from there to π/3 * radius for each door.
For this problem to be hard, you’d have to completely forget either C=2πr or three minus two is one. :smack:
A couple of years ago this problem was given as homework to my neighbor’s kid who was in 5th grade:
In the following formula, each letter stands for a digit(same letter - same digit):
FOUR + FIVE = NINE
What digit does F stand for?
I was surprised they gave this in fifth grade. Now this is a non-trivial problem. It can be solved either the long way - by finding what each letter represents, or the short way - by short-circuiting just for F. The long way, IIRC, took me something like five minutes.
The originial problem took a couple of minutes and a pen and napkin. I’d be interested in knowing how to solve the last problem. I got an answer that worked but it involved working backwards and solving for each number and I was wondering if there was an easier way.
Did the question ask for both possible values of F? Or were they okay with the kids getting just one?
I don’t know how you did it, and I imagine there are a number of different ways. If you got an answer, any answer that works, then good for you.
The way I did it amounted to:
- Determine the maximum value of F by looking at the number of digits in the sum
- Find the value of the letter R (which is very straightforward)
- Find the value of the letter O (which once you know the value of R is pretty much equally straightforward–this is assuming that each letter stands for a different digit, so R is not equal to O)
- List possible combinations of F and N (so if F is 1, N would be…), recognizing that because of step 1 there aren’t very many possibles
- List possible combinations of U and V that would give you a result ending in N
- Check to see which of those combinations work with regard to the values of R and O already determined.
(I’m trying to not give away the conclusions–if this isn’t helpful and you want to know more details, PM me)
I got it!
1 + 1 = x
-1 -1
1 = x - 1
-x -x
-x + 1 = -1
-1 -1
-x = -1 - 1
x = 1 + 1
What do I win!?
A ham sandwich!
(Congratulations, btw, and good job of showing your work.)
One of the things these rankings rarely point out is that the scores reported for the US are, pretty much, an average of the entire population of 16-18 year olds. That is, for the most part, all Americans go to high school regardless of ability or social standing. Sure, there are some societal groups that have high dropout rates, but an high school education is available to everyone. This is not true for many of the countries on that list. In many countries, unless your can afford to go to a private school, you won’t be going to high school unless you score high on standardized tests in primary school; in some countries you get moved into “trade schools”, while others, you just get to go to work. When you filter out the students that don’t have the aptitude for attacking these types of problems, of course the filtered group will have a higher average score. Give that question to US high school students that made a 30 or better on the ACT, and you would get a much different result.
excavating (for a mind)
Took me a minute or two to solve it. I’m no engineer, so that’s against me, but I’m teaching perimeter to my third graders right now, so it’s fresh in my mind.
Way I saw it, if either side-wall of the enclosure is less than a full third of the circle, air gets through, so each side wall is a third of the circle.
That’s two thirds right there taken up by walls, so the doors gotta share the remaining third. Since they’re equal, that means they’re max 1/6 of the circle each.
200 cm times a little more than 3 is a little more than 600. A sixth of that is a little more than 100. I didn’t bother figuring it out any more precisely than that.
And yes, people have been chicken littleing the state of our nation’s public educational system based on tests like this for almost exactly fifty years. Since the first time people bemoaned the lack of our children’s mathematical ability, kids raised in those terrible public schools have built the Internet, created Microsoft and Amazon and Blizzard, mapped the human genome, filed a bajillion patents, and more.
Those tests are like the drunkard who searches for his keys under the lamp post because that’s where the light is. They measure the stuff they measure not because that’s proven to be important stuff to measure, but because it’s the stuff that’s easy to measure. There’s no link between a nation’s ability to rock these tests and a nation’s ability to innovate and create and maintain a world-class economy.
Piece of cake, but then there’s this gem in the description of allowable answers:
Pi = 3 is considered a correct answer! What the fuck?
I’m sure I could have figured it out easily in high school, and probably in college, but 22 years out of high school, my geometry, trig and algebra is pretty rusty, and I didn’t know at a glance how to solve the problem.
I used to be a surveyor so I didn’t really think about it, the answer was obvious. So a few seconds. I think it would have been just as obvious at the time I was in high school.
I looked at it, thought about it for 15 seconds, and said to myself: “Screw this. I’m not in high school, why should I try to figure this out? I’ll just continue to only post to threads where I can brag about how easy geography questions are.”
So, I wouldn’t have gotten it.
AFAIK and figured out, there was only one answer: 2. What is the second one?
The other possibility is 1.
One way to set it up would be
[SPOILER]
…1970
- 1265
…3235
where
F=1, O=9, U=7, R=0, I=2, V=6, E=5, and N=3[/SPOILER]
You (or they?) left out an utterly critical constraint, which is that each letter stands for a different digit. Without that, F could be anywhere from 0 to 4.