MathDB

5

Part of 2023 MOAA

Problems(4)

2023 MOAA Speed P5

Source:

10/13/2023
Let P(x)P(x) be a nonzero quadratic polynomial such that P(1)=P(2)=0P(1) = P(2) = 0. Given that P(3)2=P(4)+P(5)P(3)^2 = P(4)+P(5), find P(6)P(6).
Proposed by Andy Xu
MOAA 2023
2023 MOAA Accuracy P5

Source:

10/13/2023
Let kk be a constant such that exactly three real values of xx satisfy x−∣x2−4x+3∣=kx-|x^2-4x+3| = k The sum of all possible values of kk can be expressed in the form mn\frac{m}{n} where mm and nn are relatively prime positive integers, find m+nm+n.
Proposed by Andy Xu
MOAA 2023
2023 MOAA Team P5

Source:

10/14/2023
Angeline starts with a 6-digit number and she moves the last digit to the front. For example, if she originally had 100823100823 she ends up with 310082310082. Given that her new number is 44 times her original number, find the smallest possible value of her original number.
Proposed by Angeline Zhao
MOAA 2023
2023 MOAA Gunga P5

Source:

10/15/2023
Andy creates a 3 sided dice with a side labeled 77, a side labeled 1717, and a side labeled 2727. He then asks Anthony to roll the dice 33 times. The probability that the product of Anthony's rolls is greater than 20232023 can be expressed in the form mn\frac{m}{n} where mm and nn are relatively prime positive integers. Find m+nm+n.
Proposed by Andy Xu
MOAA 2023