Using only pennies, nickels, dimes, and quarters, what is the smallest number of coins Freddie would need so he could pay any amount of money less than a dollar?
In a room, $2/5$ of the people are wearing gloves, and $3/4$ of the people are wearing hats. What is the minimum number of people in the room wearing both a hat and a glove?
Everyday at school, Jo climbs a flight of $6$ stairs. Joe can take the stairs $1$, $2$, or $3$ at a time. For example, Jo could climb $3$, then $1$, then $2$. In how many ways can Jo climb the stairs?
What time was it $2011$ minutes after midnight on January $1$, $2011$?
In a town of $351$ adults, every adult owns a car, motorcycle, or both. If $331$ adults own cars and $45$ adults own motorcycles, how many of the car owners do not own a motorcycle?
Bag $A$ has three chips labeled $1$, $3$, and $5$. Bag $B$ has three chips labeled $2$, $4$, and $6$. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
A fair $6$-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?
What is the tens digit of $7^{2019}$?
How many $4$-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of $5$, and $5$ is the largest digit?
In how many ways can $10001$ be written as the sum of two primes?
How many $4$-digit numbers greater than $1000$ are there that use the four digits of $2012$?
What is the units digit of $13^{2019}$?
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of $21$ conference games were played during the $2012$ season, how many teams were members of the BIG N conference?
The smallest number greater than $2$ that leaves a remainder of $2$ when divided by $3$, $4$, $5$, or $6$ lies between what numbers?
A fair coin is tossed $3$ times. What is the probability of at least two consecutive heads?
What are the sign and units digit of the product of all the odd negative integers strictly greater than $-2015$?
Among the positive integers less than $100$, each of whose digits is a prime number, one is selected at random. What is the probability that the selected number is prime?
If integer $a$, $b$, $c$, and $d$ satisfy $ad-bc=1$. Prove $a+b$ and $c+d$ are relatively prime.
Prove for any positive integer $n$, the fraction $\frac{21n+4}{14n+3}$ cannot be further simplified.
Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?
Three runners start running simultaneously from the same point on a 500-meter circular track. They each run clockwise around the course maintaining constant speeds of 4.4, 4.8, and 5.0 meters per second. The runners stop once they are all together again somewhere on the circular course. How many seconds do the runners run?
When Ringo places his marbles into bags with 6 marbles per bag, he has 4 marbles left over. When Paul does the same with his marbles, he has 3 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 6 marbles per bag. How many marbles will be left over?
In a round-robin tournament with $6$ teams, each team plays one game against each other team, and each game results in one team winning and one team losing. At the end of the tournament, the teams are ranked by the number of games won. What is the maximum number of teams that could be tied for the most wins at the end on the tournament?
Suppose that one of every $500$ people in a certain population has a particular disease, which displays no symptoms. A blood test is available for screening for this disease. For a person who has this disease, the test always turns out positive. For a person who does not have the disease, however, there is a $2\%$ false positive rate--in other words, for such people, $98\%$ of the time the test will turn out negative, but $2\%$ of the time the test will turn out positive and will incorrectly indicate that the person has the disease. Let $p$ be the probability that a person who is chosen at random from this population and gets a positive test result actually has the disease. Find $p$.