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Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

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Intersecting Circles

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

Shifting Times Tables

Stage: 3 Challenge Level: Challenge Level:1

For the Level 3 and 4 problems, start by rearranging the numbers so that they are in order. Then look at the pairs of numbers that are closest together.