Choose a numerator and a denominator from $1,2,3,4,5,6,7,8,9,10$. Many resulting fractions are equal after reduction. How many distinct reduced fractions are strictly greater than $1/2$ and strictly less than $1$?
Jericho has stickers. Grouping them in piles of 6 leaves 5 stickers, in piles of 22 leaves 21, and in piles of 14 leaves 13. What is the least possible number of stickers?
Look at the distance–time graph. Which listed interval has the highest average rate of change of distance? The vertical axis is distance (km); the horizontal axis is time (minutes).
Three brothers have a total age of 32 years. The oldest is twice as old as the youngest. The two older brothers differ in age by 3 years. How old is the youngest?
The same symbol always has the same value. Given
$$\square+\triangle+\diamond=60,\quad \triangle+\diamond+\star=44,$$
$$\diamond+\star+\square=52,\quad\triangle+\diamond+\star+\square=74,$$
find $\star+\square+\triangle$.
For example, $2^5=2\times2\times2\times2\times2$. If $4096=a^b$, find the sum of all possible values of $a$, where $a$ is a positive integer and $b$ is a whole number greater than 1.
The product of two or more consecutive positive integers is a six-digit palindrome whose first two digits are 47. What is the largest integer in the product? A palindrome reads the same backwards and forwards. Use positive integers, as intended by the source.
A lattice point has integer coordinates. Form the set of points $(a,b)$ where both $a$ and $b$ are positive integers. How many of these points lie on the line $y=-4x+8$?
Four sisters paint at the same constant rate and take turns, with no overlap or gaps. Alice finishes $1/4$ of the job; then Beth finishes $2/3$ of what is left; then Cathy finishes $3/4$ of the new remainder. Dee completes the last part in 20 minutes. How many minutes does the entire job take?
In the cryptarithm $\overline{TIC}+\overline{TAC}+\overline{TOE}=\overline{WIN}$, different letters represent different decimal digits and equal letters represent the same digit. Given $A=5$ and $O=4$, find the greatest possible value of $\overline{WIN}$. The leading digits $T,W$ are nonzero.
A mother makes $x$ cakes in 2 hours and $y$ pizzas in 3 hours. How many cakes and pizzas altogether can she make in 6 hours? Assume she makes both together, each at the same constant rate as when making it separately.
The first 73 odd whole numbers are written down. How many times does the digit 3 appear? Count every occurrence, so a number with two 3s contributes twice.
