MathDB

9

Part of 2017 AIME Problems

Problems(2)

I got 99 problems and this is one.

Source: 2017 AIME I #9

3/8/2017
Let a10=10a_{10} = 10, and for each integer n>10n >10 let an=100an−1+na_n = 100a_{n - 1} + n. Find the least n>10n > 10 such that ana_n is a multiple of 9999.
AIMEAIME I2017 AIME Inumber theoryIntermediate Number Theory
Moby Deck of Cards

Source: 2017 AIME II #9

3/23/2017
A special deck of cards contains 4949 cards, each labeled with a number from 11 to 77 and colored with one of seven colors. Each number-color combination appears on exactly one card. Sharon will select a set of eight cards from the deck at random. Given that she gets at least one card of each color and at least one card with each number, the probability that Sharon can discard one of her cards and still have at least one card of each color and at least one card with each number is pq\frac{p}{q}, where pp and qq are relatively prime positive integers. Find p+qp+q.
AMCAIMEAIME II