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Pinned Squares

The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a 5 by 5 board?

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Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at the number of diagonals?

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AP Rectangles

An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?

Hot Pursuit

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?