Combinatorics
There are 10 TAs in New York Math Circle. They line up to get to Heytea. How many ways are there for them to line up?
Double points if you compute it.
What is 10! or 3628800?
A number x has a remainder of 2 when divided by 5, and a remainder of 3 when divided by 6. Find the smallest positive value of x.
Calculate the y-intercept of the line with points (3, 5) and (7, 11). Express you answer as a decimal to the nearest tenth.
What is 0.5?
If 12 + r2 = 17, then what is (10/r)2 ?
What is 20?
Kyle is taking the AMC10, a test with 25 questions. A correct answer is worth 6 points, an incorrect answer receives 0 points, and an unanswered question receives 1.5 points. Kyle didn't study so he will guess on each question. Aviv, Kyle's little brother, is also taking the test, but broke arms on the way there so he left his test blank. On average, who will get the better score and by how much?
Aviv, and by 7.5 points.
Selin likes running and wants to run 15 miles this summer. She can run either 2 miles or 3 miles a day. In how many ways can she run the 15 miles?
What is 28?
The six-digit number 20210A is prime when A equals this digit.
What is 9?
Find x+y, if 5x + 8y = 67 and 2x-y =31.
What is 14?
What is the product of all integers from -10 to 10 inclusive?
What is 0?
Where did Sandy get her expensive gaming laptop from?
What is Costco?
How many ways can you distribute 10 cookies among 3 distinct children if each child must have a different number of cookies?
What is 48?
Kyle selects a random integer n from 1 to 100. What is the probability that n2 - 1 is divisible by 5? Write it as a percentage.
What is 40%?
Mary has taken four tests and has a test avg of 94. Her parents want her to maintain at least 90. What is the lowest score Mary can get on her next test while keeping her avg at least 90?
What is 74?
how old is kyle
what is 19
When 7 fair standard 6-sided dice are thrown, the probability that the sum of the numbers on the top faces is 10 can be written as n/67, where n is a positive integer. What is n?
What is 84?
DAILY DOUBLE!!!
When N is written in base 2, 3, and 5, it has a last digit of 0. When written in base 7 and 8, it has a last digit of 2. What is the smallest such N?
What is 450?
Factor by grouping: 12a^3 - 9a^2 + 4a - 3
What is (3a^2 +1)(4a-3)?
Find the area of the region bounded by: y > 0, y < x, and x2 + y2 < 16.
What is 2π?
In how many years will the ratio of Aviv's age to Sandy's age be 66/67?
What is 118?
How many ways are there to tile a 2 × 7 rectangle with 1 × 2 tiles?
What is 21?
Find the smallest positive integer x such that 6x has twice as many divisors as x.
If x+y = 35 - xy and (x+1)(y+2) = 48, find x.
What is 11?
What is the probability that a random permutation of MATH has exactly 2 letters in the same place as a random permutation of the word THAT? Express your answer as a common fraction.
What is 1/6?
Kyle starts on one corner of a 1m x 1m square and wants to get to the (diagonally) opposite corner. However, the lights are turned off and Kyle can't see anything, so he will randomly choose an adjacent corner and walk to it. What is the probability that Kyle will get to the opposite corner after walking more than 6 meters? Express your answer as a common fraction.
What is 1/8?