MathDB

p1 How many two-digit positive integers with distinct digits satisfy the conditions that 1) neither digit is

0

, and 2) the units digit is a multiple of the tens digit?
p2 Mirabel has

47

candies to pass out to a class with

n

students, where

10\le n < 20

. After distributing the candy as evenly as possible, she has some candies left over. Find the smallest integer

k

such that Mirabel could have had

k

leftover candies.
p3 Callie picks two distinct numbers from

\{1, 2, 3, 4, 5\}

at random. The probability that the sum of the numbers she picked is greater than the sum of the numbers she didn’t pick is

p

p

can be expressed as

\frac{a}{b}

for positive integers

a, b

with

gcd (a, b) = 1

. Find

a + b

Problem Statement