Difference between revisions of "2021 April MIMC 10"
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[[2021 April MIMC 10 Problems/Problem 2|Solution]] | [[2021 April MIMC 10 Problems/Problem 2|Solution]] | ||
| + | ==Problem 3== | ||
| + | 3. Find the number of real solutions that satisfy the equation | ||
| + | <math>(x^2+2x+2)^{3x+2}=1</math>. | ||
| − | + | <math>\textbf{(A)} ~0 \qquad\textbf{(B)} ~1 \qquad\textbf{(C)} ~2 \qquad\textbf{(D)} ~3 \qquad\textbf{(E)} ~4</math> | |
| + | |||
| + | [[2021 April MIMC 10 Problems/Problem 3|Solution]] | ||
| + | |||
| + | 4. Stiskwey wrote all the possible permutations of the letters <math>AABBCCCD</math> (<math>AABBCCCD</math> is different from <math>AABBCCDC</math>). How many such permutations are there? | ||
| + | |||
| + | <math>\textbf{(A)} ~420 \qquad\textbf{(B)} ~630 \qquad\textbf{(C)} ~840 \qquad\textbf{(D)} ~1680 \qquad\textbf{(E)} ~5040</math> | ||
Revision as of 22:54, 20 April 2021
Problem 1
What is the sum of 
?
Problem 2
Okestima is reading a 
page book. He reads a page every 
minutes, and he pauses 
minutes when he reaches the end of page 90 to take a break. He does not read at all during the break. After, he comes back with food and this slows down his reading speed. He reads one page in 
minutes. If he starts to read at 
, when does he finish the book?
Problem 3
3. Find the number of real solutions that satisfy the equation
.
4. Stiskwey wrote all the possible permutations of the letters 
( is different from 
). How many such permutations are there?
