The equilateral triangle, circle, and square shown above have equal areas. Which has the largest perimeter?

\(\)

**Note:** The diagram is not drawn to scale.

I want to fill in the eight circles below using each of the numbers 1, 2, 3, 4, 5, 6, 7, 8 **exactly once**. Additionally, consecutive numbers--e.g. \((1, 2)\) or \((5,6)\)-- **cannot** be placed in circles which are connected by a line segment.

Is this possible, and if so, what is the sum of the two numbers in the middle?

On an \(8 \times 8\) chessboard, can a knight move from one corner to the opposite corner, visiting each and every remaining square exactly once on its way there?

\(\)

**Clarification:** A knight can move to a square that is either two squares away horizontally and one square vertically, or two squares vertically and one square horizontally.

Hasmik invited several guests, and she knows that there will either be 7 or 8 people at the party. She wants to slice up a big pie into smaller pieces, not necessarily of the same size, such that regardless of how many people show up, she can serve the entire pie evenly to everyone.

What is the minimum number of pieces she will need to slice the big pie into?

×

Problem Loading...

Note Loading...

Set Loading...