Recursion/Combinatorics/
Probability
Probability
There are 12 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
12! or 479001600
Three of the numbers in the set {23, 24, 25, 26, 27, 28, 29} have a product of 16675. Compute the sum of the three numbers.
77
Calculate the y-intercept of the line with points (3, 5) and (7, 11)
The lengths of the sides of right triangle ABC form an arithmetic sequence. If the shorter leg has a length of 10, compute the area of ABC.
200/3
Decode this: 9 12 9 11 5 13 1 20 8
I Like Math
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?
28
The six-digit number 20210A is prime for only one digit A. What is A?
9
Find x+y, if 5x + 8y = 67 and 2x-y =31
14
The vertices of a parallelogram are A(1, 3), B(4, 8), C(6, 2) and D(x, y). Compute the area of parallelogram ABCD.
28
DAILY DOUBLE!!!
How many sets of two or more consecutive positive integers sum to 60?
3
Jayson decided to Triple Major at Stony Brook. How many ways can he take 5 math classes: Combinatorics, Differential Equations, Graph Theory, Linear Algebra, and Analysis on Manifolds in an 8-period day?
6720
Compute the unit digit of 4^1 - 6^7.
2
Factor by grouping: 12a^3 - 9a^2 + 4a - 3
(3a^2 +1)(4a-3)
Sunny draws a triangle with side lengths 8, 15, and 17. He then draws a rectangle with the same perimeter and area as the triangle. If the diagonal of the rectangle has length L, what is L^2?
280
Three consecutive integers multiply to 2730. What is the sum of these integers?
42
There are five boroughs in New York City. Every day, Jayson randomly picks a borough that he is not currently in and takes the MTA there (Ew). He starts outside of the city in New Jersey (Also Ew). What is the probability that after five days, he will have gone to all five boroughs?
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?
450
Find the smallest positive integer x such that 6x has twice as many divisors as x
12
Trapezoid ABCD has AB parallel to CD and AD perpendicular to AB. If AB = 8, AD = 4, and CD = BC, find the area of the trapezoid.
26
Ethan wants to color each cell of a 2x2 grid either red, yellow, green, or blue. How many ways can he do this so that no two cells that share an edge are colored the same color?
84
How many ways are there to tile a 2x7 rectangle with 1x2 tiles?
21
Find the smallest positive integer n such that n is divisible by exactly 25 different positive integers.
1296
Let D, M, I be nonnegative integers such that D + M + I = 24. What is the maximum value of DMI + DM + DI + MI
704
Jayson has two ice cream cones. The first is three times as tall as the second, but its radius is only half as long as the radius of the second. The positive difference between the cones’ volumes is 40π, so the sum of their volumes is Pπ. Compute P.
280
What is the sum of the TAs' and Instructors' ages?
Double, if you can guess our individual ages
59
Jayson: 24
Selin: 19
Kevin: 15