2021 April MIMC 10
What is the sum of ?
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?
Find the number of real solutions that satisfy the equation .
Stiskwey wrote all the possible permutations of the letters ( is different from ). How many such permutations are there?
5. Given , Find .
A worker cuts a piece of wire into two pieces. The two pieces, and , enclose an equilateral triangle and a square with equal area, respectively. The ratio of the length of to the length of can be expressed as in the simplest form. Find .
Find the least integer such that where denotes in base-.
In the morning, Mr.Gavin always uses his alarm to wake him up. The alarm is special. It always rings in a cycle of ten rings. The first ring lasts second, and each ring after lasts twice the time than the previous ring. Given that Mr.Gavin has an equal probability of waking up at any time, what is the probability that Mr.Gavin wakes up and end the alarm during the tenth ring?
Find the largest number in the choices that divides .
If and , find .
How many factors of is a perfect cube or a perfect square?
Given that , what is ?
Given that Giant want to put green identical balls into different boxes such that each box contains at least two balls, and that no box can contain or more balls. Find the number of ways that Giant can accomplish this.
James randomly choose an ordered pair which both and are elements in the set , and are not necessarily distinct, and all of the equations:
are divisible by . Find the probability that James can do so.