Exploring and noticing

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?

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?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

How many 10-digit numbers containing only 1s, 2s and 3s can you write?

Can you solve the clues to find out who's who on the friendship graph?

I'd be very surprised if I had three children all with the same birthday, but I read in the paper that it happened to one family...