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| − | ==Instructions==
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| − | 1. All rules of a regular AMC 10 apply.
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| − | 2. Please submit your answers in a DM to me (Lcz).
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| − | 3. Don't cheat.
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| − | Here's the problems!
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| − | ==Problem 1==
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| − | Find the value of <math>2^{0+2+1}+2+0(2+(1))+20(21)</math>.
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| − | <math>\textbf{(A)}\ 8 \qquad\textbf{(B)}\ 426 \qquad\textbf{(C)}\ 428 \qquad\textbf{(D)}\ 430 \qquad\textbf{(E)}\ 432</math>
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| − | ==Problem 2==
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| − | If <math>|x-2|=0</math>, and <math>|y-3|=1</math>, find the sum of all possible values of <math>|xy|</math>.
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| − | <math>\textbf{(A)}\ 0 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 8 \qquad\textbf{(D)}\ 12 \qquad\textbf{(E)}\ 16</math>
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| − | ==Problem 3==
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| − | What is <math>1*2+2*3+3*4+4*5+5*6+6*7+7*8</math>?
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| − | <math>\textbf{(A)}\ 84 \qquad\textbf{(B)}\ 120 \qquad\textbf{(C)}\ 138 \qquad\textbf{(D)}\ 150 \qquad\textbf{(E)}\ 168</math>
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| − | ==Problem 4==
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| − | Find the sum of all ordered pairs of positive integer <math>x</math> and <math>y</math> such that
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| − | (1) <math>|x-y| \geq 0</math>
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| − | (2) <math>x,y \leq 3</math>
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| − | (3) <math>xy \leq 8</math>
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| − | <math>\textbf{(A)}\ 24 \qquad\textbf{(B)}\ 27 \qquad\textbf{(C)}\ 30 \qquad\textbf{(D)}\ 36 \qquad\textbf{(E)}\ 39</math>
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| − | ==Problem 10==
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| − | Jack and Jill play a (bad) game on a number line which contains the integers. Jack starts at <math>-1</math>, and Jill starts at <math>18</math>. Every turn, the judge flip a standard six sided die. If the number rolled is a square number, Jack moves to the right <math>10</math> units. Otherwise, Jill moves to the left <math>5</math> units. Find the probability for which Jack and Jill pass each other for the first time in <math>3</math> moves.
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| − | <math>\textbf{(A)}\ 4/27 \qquad\textbf{(B)}\ 2/9 \qquad\textbf{(C)}\ 1/3 \qquad\textbf{(D)}\ 4/9 \qquad\textbf{(E)}\ 2/3</math>
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| − | ==Problem 13==
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| − | How many <math>4</math>-digit integers contain a substring of digits that is divisible by <math>4</math>? (For example, count in <math>1532</math> because it contains <math>32</math>, but don't count in <math>1734</math>.)
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