Combinatorics
a+b+c = 19
a^2 + b^2 + c^2 = 2019
Find ab + bc + ca
-829
When 3361 and 4705 is divided by natural number n, the remainders are both 1. Find the largest possible value of n.
672
Three vertices of ABC are (-2,1), (3, -1), (5, 1). Find th equation of the median passing through A.
y = -1/6x + 4/6
N is a positive integer such that n/2019 rounds to 6. Find the number of possible values of n.
2019
69421
Peter Cheng, Bryan Tom, Daniel Gusak, and James Gikas are watching a movie on Valentine's Day. Peter and Bryan Tom have to sit together, and Daniel and Peter can't sit together. How many ways can they sit together?
8, Peter gave this answer so if it is wrong blame him I'm too lazy to check
2sqrt5/5
sqrt2/2
-2sqrt5/5
-sqrt2/2
Find the remainder when 7^2019 * 9^2020 is divided by 31
9
Each of Aiden, Bella and Chris prepared a box for Dyland. Dylan's birthday present is in one of the boxes. The teacher in advance told Dyland how many of them lied.
Aiden, "The present is in my box"
Bella, "The present is in Chris's box"
Chris, "The present is not in Aiden's box"
Dylan, under teacher's clue successfully deduced which box contains the present. Whose box is the present in?
Chris