In the cryptarithm $DUCK+DUCK=GOOSE$, different letters represent different digits and repeated letters represent the same digit. What is the least possible value of the three-digit number $GOO$? Leading digits are nonzero.
A circle of radius 14 cm and a circle of radius 21 cm overlap in the crosshatched region shown. The overlap has area $580\text{ cm}^2$. What is half the total area, in $\text{cm}^2$, of the two regions without crosshatching? Use $\pi=\frac{22}{7}$.
Thirty-six points form a unit-square array as shown. Figure ABCDE consists entirely of straight-line segments with vertices A, B, C, D and E. Find the sum of its interior angles, in degrees.
In triangle ABC, point D lies on side AC with $AD=4$ and $CD=7$. Triangle ABD has area 20 square units. What is the area of triangle ABC, in square units?
The figure is formed by overlapping three rectangles measuring 2 cm by 6 cm. An ant completes one trip around its perimeter, moving at 1 cm/s on horizontal segments and 2 cm/s on vertical segments. How many seconds does the trip take?
Sasha wants an image to fit exactly and snugly into a box on her computer screen without squishing or stretching its proportions. The original image is $1\frac12$ inches wide and $2\frac14$ inches tall. The box is 4 inches wide. How tall must it be? All options are in inches.
A team won 2 of its first 9 games and lost 25% of its remaining games. Overall, it won $\frac23$ of all its games. How many games did it lose? Assume every game ends in a win or a loss, with no draws.
Ten standard dice are rolled and their top-face values are added. Each die has the six face values 1, 2, 3, 4, 5 and 6. How many different sums are possible?
What is the difference between the sum of the multiples of 3 less than 200 and the sum of the multiples of 5 less than 250? Here multiples are positive; subtract the second sum from the first.
A child gets 10 dollars in pocket money each day. He saves 1 dollar on the first day, 2 dollars on the second, 3 dollars on the third, 4 dollars on the fourth, and so on. On which day will he first have enough saved to buy his sister a 50-dollar school bag?
An M-shaped MOEMS tile is made from a 5 by 5 square by removing two 4 by 1 rectangles, as shown. Jimmy wants to place as many tiles as possible on a 6 by 42 game board without overlap. What is the maximum number of tiles? Tiles must lie entirely on the board and may be rotated or flipped.
All six faces of the cube shown are painted black. It is then cut into 64 identical smaller cubes. How many smaller cubes have black paint on at least two faces?
