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Multiplying the first term, $\frac{1}{100}$, by the whole of $(\frac{1}{100} + \frac{1}{10000} + \frac{1}{1000000} + \dots)$. ) yields the repeating decimal $0.00\overline{01}$

Multiplying the second term yields $0.0000\overline{01}$, and so forth. Thus, the decimal looks like so:

$0.000010203040506070809101112131415\dots969799$ -- note that $98 + 99 + 100$ at the end turns into $990000$.

Adding it up, the sum of the first $9$ natural numbers occurs $10$ times, so that's $450$. Then the digit $1-9$ appears as the "tens place" $10$ times each, so that's another $450$. Subtract $8 + 9 = 17$ since $98$ isn't counted to get $883$ as the answer. $\blacksquare$

AMC12....expecting a 118.5, enough to make the AIME. During the test, I only focused on the first 20 questions(as I mentioned in my strategy), I skipped number 8 on due to the confusing wording of the problem, later I found out all of other participants in my school was able to do that problem. Next there was number 18, which twisted up my brain......

Other than these, I feel satisfied since I didn't leave any counting and geometry problems blank :)

I got a 132, but I made a stupid mistake on number 4. It was really easy this time; previously, I had scored 1.5 less than the cutoff almost every time.

I got 130.5 on AMC 10. Made a stupid mistake on number 4 (multiplied by 2). Finished the first 22, missed one. I heard from my friend that #23 was easy, but otherwise, I think I did well. The AMC answers are all on AoPS, so you can go on there to check.
Well, I'm taking the AMC 12B next week. Hopefully, I can get at least a 110.

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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## Comments

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TopNewestYou can find the answer key online with a google search. I exceeded my expectations! The test had beautiful problems, like #25, (which I skipped)

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Oh Thanks :)

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The AIME cutoff's going to have to be 120 this year.

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I'm mad at myself for making FOUR stupid mistakes:

Forgot to add the original 35 miles (#11)

For the palindrome question, I added all $abc$ rather than $abcba$

For the arith/geo sequence question, forgot $a<b<c$

For question 24 with the absolute values (which was stupidly easy and didn't deserve to be question 24) I thought $f_0 (x)$ was $f_1 (x)$!

But it's okay. I'm taking the 12B next week too. (I got a predicted 102 on this one, sadly)

Favorite problems: Question 21 and 23.

Question 21 because it's one of those "looks hard but isn't" questions

Question 23 because it's a great question.

Solution 23: Note that $\frac{1}{99} = .\overline{01} = (\frac{1}{100} + \frac{1}{10000} + \dots$, so $\frac{1}{99^2} = (\frac{1}{100} + \frac{1}{10000} + \frac{1}{1000000} + \dots) (\frac{1}{100} + \frac{1}{10000} + \frac{1}{1000000} + \dots)$.

Multiplying the first term, $\frac{1}{100}$, by the whole of $(\frac{1}{100} + \frac{1}{10000} + \frac{1}{1000000} + \dots)$. ) yields the repeating decimal $0.00\overline{01}$

Multiplying the second term yields $0.0000\overline{01}$, and so forth. Thus, the decimal looks like so:

$0.000010203040506070809101112131415\dots969799$ -- note that $98 + 99 + 100$ at the end turns into $990000$.

Adding it up, the sum of the first $9$ natural numbers occurs $10$ times, so that's $450$. Then the digit $1-9$ appears as the "tens place" $10$ times each, so that's another $450$. Subtract $8 + 9 = 17$ since $98$ isn't counted to get $883$ as the answer. $\blacksquare$

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i tooko the 10A, and i got a 114. Not as good as I wished it could be, but I am overall satisfied

@Michael tong- you're 23, how you take the amc12

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read my profile -- "I'm 17, not 23!"

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AMC12....expecting a 118.5, enough to make the AIME. During the test, I only focused on the first 20 questions(as I mentioned in my strategy), I skipped number 8 on due to the confusing wording of the problem, later I found out all of other participants in my school was able to do that problem. Next there was number 18, which twisted up my brain......

Other than these, I feel satisfied since I didn't leave any counting and geometry problems blank :)

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I got a 132, but I made a stupid mistake on number 4. It was really easy this time; previously, I had scored 1.5 less than the cutoff almost every time.

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On the AMC 10, I did my modular arithmetic wrong and got #2 wrong...

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lol same here :P

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I feel dumb... Made a dumb arithmetic mistake on #17 [36+9=42] and ended up with 112.5

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I got 130.5 on AMC 10. Made a stupid mistake on number 4 (multiplied by 2). Finished the first 22, missed one. I heard from my friend that #23 was easy, but otherwise, I think I did well. The AMC answers are all on AoPS, so you can go on there to check. Well, I'm taking the AMC 12B next week. Hopefully, I can get at least a 110.

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