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| 20 Feb 2013 10:43 AM |
Anyone else take it? I didn't think it was too hard this year. I answered 10/25.
I'll post a few of the questions when I get home later tonight. |
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| 20 Feb 2013 12:59 PM |
| FYI AMC means American Math Competition |
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| 20 Feb 2013 01:35 PM |
| We have UKMT over here in the UK. |
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810CC0
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| 20 Feb 2013 01:50 PM |
I got 20/25 on the AMC 8
I wonder when the AMC 10 and 12 are |
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Sorcus
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| 20 Feb 2013 02:43 PM |
I go to AMC all the time to watch movies.
~Sorcus |
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| 20 Feb 2013 02:49 PM |
no hes talking about the American Math Competition
- Danster5oo's secondary alternative account |
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DannyCore
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HotThoth
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| 20 Feb 2013 03:18 PM |
I used to take those; they were fun, but I didn't like the time pressure on them. I took them mainly just so I could take the AIME, so eventually I switched over to qualifying by USAMTS (pretty much 0 time pressure whatsoever).
I much prefer those seemingly impossible problems, but you got a lot of time to think about it, so you can really get into it and every time you get one you'd get that feeling of "WHEEE!" I think AIME was the first time math went from being something I just liked and was good at to being something I found as being really cool/fun/exciting/challenging/awesome.
- HotThoth
~ Think happy Thoths ~ |
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| 20 Feb 2013 03:27 PM |
| I agree with HotThoth. The UKMT is timed, but the later questions are hard and if you get them, you can silently and invisibly jump out of your seat and scream at the other people doing it. Everybody else left feeling negative and that they had failed, whereas I felt thrilled and really good about the challenge. |
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| 20 Feb 2013 04:19 PM |
Since the test was this morning and they let us keep the booklet, I think it's safe to discuss these now.
It's 25 questions but I'll only list a few. Starting with an easy one
Real numbers x and y satisfy the equation x^2 + y^2 = 10x - 6y -34 what is x + y? A) 1 B)2 C)3 D)6 E)8
What is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12! ? A)5 B)7 C)8 D)10 E)12
Alex has 75 red tokens and 75 blue tokens. There is a booth where alex can give two red tokens and receive in return a silver token and a blue token, and another booth where alex can give three blue tokens and receive in return a silver token and a red token. Alex continues to exchange tokens until no more exchanges are possible. How many silver tokens will Alex have at the end? A)62 B)82 C)83 D)102 E)103
Two bees start at the same spot and fly at the same rate in the following directions. Bee A travels 1 foot north and then 1 foot east, then one foot upwards, and then continues to repeat this pattern. Bee B travels 1 foot south, then 1 foot west and then continues to repeat this pattern. In what directions are the bees traveling when they are exactly 10 feed apart? A) A east, B west B) A north, B south C) A north, B west D) A up, B south E) A up, B west
More to come later
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| 20 Feb 2013 04:22 PM |
Bernardo chooses a three digit positive integer N and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers. Treating the two numbers as base-10 integers, he adds them to obtain an integer S. For example, if N = 749, Bernardo writes the numbers 10,444 and 3,245, and LeRoy obtains the sum S = 13,689. For how many choices of N are the two rightmost digits of S, in order, the same as those of 2N? A) 5 B) 10 C) 15 D) 20 E) 25
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| 20 Feb 2013 04:23 PM |
| Maybe stravant will have fun with these. |
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HotThoth
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| 20 Feb 2013 04:33 PM |
So far my favorite is the first one; that's actually a really cool trick, and I haven't seen anything like that before. Really glad you shared that!
- HotThoth
~ Think happy Thoths ~
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| 20 Feb 2013 05:13 PM |
| I've been thinking about the first one for a while. I can't think of a way to answer it. |
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DannyCore
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| 20 Feb 2013 05:15 PM |
well, pre, you're going to have a limited amount of time to answer each question so... idk |
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| 20 Feb 2013 05:16 PM |
JUST TELL ME HOW TO GET ANSWER
Time is subjective. |
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Seranok
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| 20 Feb 2013 05:28 PM |
| HotThoth, would you mind explaining why you find mathematics interesting? |
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| 20 Feb 2013 05:29 PM |
"Bernardo chooses a three digit positive integer N and writes both its base-5 and base-6 representations on a blackboard. Later LeRoy sees the two numbers. Treating the two numbers as base-10 integers, he adds them to obtain an integer S. For example, if N = 749, Bernardo writes the numbers 10,444 and 3,245, and LeRoy obtains the sum S = 13,689. For how many choices of N are the two rightmost digits of S, in order, the same as those of 2N?"
This seems more like a logic puzzle than a math problem. I like it. |
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HotThoth
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| 20 Feb 2013 05:33 PM |
@ Pre: Start with completing the square-- see where that gets you... lemme know if you need any more hints.
In general, two variables one equation is NOT a solvable problem. So this means that either there is a special trick such that you can solve for specifically what is asked (so like you can rearrange it to get x+y = 10 even if you can't solve for x or y), or else there's an even cooler trick to let you actually solve for x and y somehow (in this case), or else it's impossible :).
- HotThoth
~ Think happy Thoths ~ |
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| 20 Feb 2013 06:39 PM |
I tried those and immediately went "Ugh, I hate this."
Don't get me wrong, I like math, but the limits of mathematics are the reason I switched to programming. |
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HotThoth
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Seranok
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| 20 Feb 2013 07:03 PM |
I wouldn't say math is more limited than programming, quite the opposite.
But I do find just general "math for the sake of math" quite boring. |
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HotThoth
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| 20 Feb 2013 07:12 PM |
And they both have their appeals. I love CS for the ability to take an idea and make it into a physical, tangible thing, and math has a very different appeal.
Time for an Essay on the Philosophy of Math!
The way I think of it is a lot like the line "It is not the spoon that bends, but your mind." The truth of a statement or expression never changes; the entire field of mathematics is really the science of changing how you look at something until you understand it (or an aspect of it) fundamentally.
So take something like "x - 1000 > 0". It's generally very intuitive that it must be true that x is positive; you could rework the expression (add 1000 to both sides), use 1000 > 0 and combine inequalities to actually get "x > 0", but the cool part about math like this is that you're not changing anything else ever; just the way you look at it. For someone with crazy mathematical intuition, maybe it's just as obvious that given (x^2 + y^2) = 10x - 6y - 34 it must be the case that x = 5. And the more you get into different branches of math, it becomes not just a tool for shaping how you view simple equations, but rather a tool for how you view/formulate/explore everything (even things which don't or can't ever exist). And oddly enough, even those things which can never exist can still have very important and useful implications for the real world (in an almost Plato's Cave - like manner).
Maybe that explains some of why I grew to really love it? Oh, and also I like puzzles. So... it's probably more that actually.
- HotThoth
~ Think happy Thoths ~
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Garnished
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| 22 Feb 2013 09:07 AM |
I'm far more concerned with the exchange between myself and the computer, i.e. getting my logic to turn into a comprehensible system of inter-working parts.
I get that math's important, and I've already worked on learning a bit more than my teachers are willing to share with me...
Meh, I just don't like things I can't manipulate. It makes whatever-it-is seem useless to me. |
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