A rectangular park measures 100 m by 50 m. It is fenced with a stone wall, except for a steel gate 2 m wide along the perimeter. The wall and gate are both 3 m high. Stone costs 23 dollars per square metre and steel costs 17 dollars per square metre. Find the total cost in dollars, using the area of the fencing material once (not both faces).
For fidelity, the original options were A: 10384; B: 6900; C: 20700; D: 456; E: 20615. This edition asks for the calculated amount rather than an option letter.
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.
A steel cuboid is reshaped into a cube. Initially, its length, breadth, and depth were 270 cm, 100 cm, and 64 cm respectively. Find the sum of digits of the surface area of the cube.
Assume no steel is lost or added and neither shape contains voids. Use the numerical surface area in square centimeters.
Faye and Ingrid are fruit vendors. Faye has 21 more fruits than $1\frac12$ times Ingrid’s number of fruits. Together they have 216 fruits. How many fruits does Faye have?
In the following cryptarithm, each different letter represents a different digit. Assuming a number cannot start with 0, find the last three digits of the smallest possible sum. For example, if your answer is 1234, write 234.
**Input:** Enter only the final three digits of the minimum sum.
Find the smallest integer which, when divided by 7, gives a remainder of 0, but when divided by 10 gives a remainder of 1.
Editorial clarification: in this self-study version, seek the smallest positive integer. Over all signed integers, the original wording has no smallest solution.
$2^{400}$ can be written as a repeated product of the number 16: $\underbrace{16\times16\times16\times\cdots\times16}_{n\text{ factors}}$. What is the value of $n$?
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.
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?
The numbers 123456789 and 987654321 are added. This sum is divided by a single-digit number, leaving no remainder. How many possible single-digit numbers could have been used?
Here “single-digit number” means a positive digit from 1 to 9.
The place cards shown are folded along the dotted lines so that only a number or a letter is visible. Chrissy enters the room and sees all six cards, some showing numbers and some showing letters. The visible numbers sum to 11. How many different sets of numbers are possible?
