Ashley has a paper rectangle measuring 8 cm by 12 cm. She folds it in half twice, first vertically and then horizontally. The new rectangle looks like the original but smaller. What is the area of the new smaller rectangle in $\mathrm{cm}^2$?
The scale shows a rectangle, a triangle and an oval with total weight 20 kg. The rectangle weighs 2 kg more than the triangle. The oval weighs 3 kg less than the triangle. What is the weight of the rectangle, in kilograms?
Each letter represents a different digit in the addition below. What is the least possible value of the three-digit number SUM? A cannot be zero. The four rows are ADD + ADD + ADD + ADD = SUM; each word denotes a three-digit number.
A solid brick is formed by gluing together eighty $1\times1\times1$ cubes. The brick has as little surface area as possible. The two faces with the least area are painted blue. What is the number of square units in the area of one blue face?
Here “brick” means a completely filled rectangular prism with whole-number side lengths.
Enter only the whole-number answer, without units.
Each different letter represents a different digit in the six-digit numbers below, and B is not zero. Find the last three digits of the smallest possible sum. For example, if a sum is 12345, enter 345.
**Solution-derived reconstruction:** the question's cryptarithm is missing in the source. BETTER + BITTER + BATTER + BUTTER is reconstructed from its worked solution. The original row order is unknown; row order does not affect the sum.
Enter exactly three digits, including a leading zero if needed.
Tiffany looked at a clock and realized that the number of hours passed since midnight was five times the number of hours remaining until noon. What time did the clock show 1 hour ago?
Given $\square+\triangle+\diamond=30$, $\triangle+\diamond+\star=22$, $\diamond+\star+\square=26$, and $\triangle+\diamond+\star+\square=37$, find $\star+\square+\triangle$.
Adam can paint a classroom in 6 hours. Ben can paint the same classroom in 12 hours. If they work together, each at their own rate, how many hours will they take to paint the classroom?
Raziya started with the structure below, fully packed all the way to the back of the top stairs. She added similar unit cubes to form a packed staircase, 10 steps high. Each unit cube measures $1\times1\times1$ cm. The source mentions cubes filling a box with dimensions $3\times11\times10$ cm and asks for the length (width) of each step.
**Editorial interpretation for this question:** use that box volume as the TOTAL number of cubes in the final staircase, including cubes already present, not as the number added. Each step rises 1 cm and has a tread depth of 1 cm; all steps have the same width. Find that width in cm.
