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Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?

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What are the missing numbers in the pyramids?

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A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you the last two digits of her answer. Now you can really amaze her by giving the whole answer and the three consecutive numbers used at the start.

AP Rectangles

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

An AP rectangle is one whose area is numerically equal to its perimeter. For example the rectangle 10 units by 2.5 units has area 25 square units and perimeter 25 units. If you are given the length of a side can you always find an AP rectangle with one side the given length? Explain your answer.