Exploring and noticing

A pattern repeats every six symbols. What are the 100th and 101st symbols?

Weekly Problem 51 - 2016
Pegs numbered 1 to 50 are placed in a row. Alternate pegs are knocked down, and this process is repeated. What is the number of the last peg to be knocked down?

By drawing 5 horizontal and four vertical lines, one can form 12 rectangles. What is the greatest number of rectangles that can be formed by drawing 15 lines?

Can you find the connections between linear and quadratic patterns?

There are unexpected discoveries to be made about square numbers...

Can you figure out how sequences of beach huts are generated?

What is special about the difference between squares of numbers adjacent to multiples of three?

What happens when you add a three digit number to its reverse?