colinqiu

6 Questions
1 Answers

0

10

3

+27

Number Theory: HELP!!

If a, b, and c are positive integers less than 13 such that:
2ab + bc + ca ≡ 0 (mod 13)
ab + 2bc + ca ≡ 3abc (mod 13)
ab + bc + 2ca ≡ 8abc (mod 13) read more ..

colinqiu Jun 23, 2024

0

6

2

+27

Expected Value

A standard deck of cards contains 52 cards. These 52 cards are arranged in a circle, at random. Find the expected number of pairs of adjacent cards that are both hearts.
Please help quickly!
Any help is appreciated!

colinqiu May 22, 2024

0

15

1

+27

CPhill, Please!

What is the sum of all positive integers "q" such that (n^7 - n^3)/q is an integer for every positive integer n < 2021?
Thanks in advance!

colinqiu May 21, 2024

0

9

1

+27

Help!

Six teams play a single round-robin tournament, in which each team plays every other team exactly once, there are no ties, and for each team, the probability of winning any given game is 1/2. What is the probability that at least two different teams finish read more ..

colinqiu May 14, 2024

+1

13

1

+27

Counting Problem

How many ways are there to color the 4x4 grid so that each unit square is red, blue, green or yellow, and so that each unit square is the same color as exactly two of the unit squares that share a side with it?
Thanks in read more ..

colinqiu May 14, 2024

0

13

1

+27

Hard Counting and Probability

A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.
Thanks read more ..

colinqiu May 9, 2024

+27

0

I want a helpful solution, I'm not trying to brute force it with Wolfram Alpha. Thanks though!

colinqiuJun 24, 2024