Peegue's Puzzle Page Welcome to the ninth edition of Peegue's Puzzle Page. Time time around, Peegue has a number of mathematical pattern puzzles for you. Don't try to count your way though these. Try instead to do just a few steps, and see if you can recognize a simple pattern that will help you find the solution in a flash.

Pattern 1

One the first day, Peegue receives one gold star. On the second day, Peegue receives another three gold stars (for a total of four). On the third day, Peegue receives another five gold stars. Each day the number of new gold stars that Peegue receives increases by two (seven gold stars on Day 4, nine gold stars on Day 5, ...). How many gold stars will Peegue have (in total!) after 1000 days?

Pattern 2

Gold stars are laid out in the illustrated order to create a giant pyramid shape. Notice that, for example, the 8th star is the 4th star in its row. How far into its row (counting from the left) is the 10000th gold star?

Pattern 3

A red coin is placed on the ground, then surrounded by a square of eight orange coins, then surrounded by a square of sixteen yellow coins. So far, 25 coins have been used. If this pattern continues (cycling through the colours of the rainbow: red, orange, yellow, green, blue, indigo, purple, and back to red), what colour is the 10000th coin used?

If you think you have the answers (or you -gulp!- give up), you can send Peegue an e-mail at peegue@midnightsynergy.com. You will receive an automated reply with the link to the solutions. (Make sure that you add Peegue to your address-book if you use a spamfilter, so that the reply doesn't land in your junk folder).