When working on mathematical tasks, you may sometimes discover unexpected results that take you by surprise. In this feature, we have chosen some problems that we hope will astonish and amaze you.

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Try out some calculations. Are you surprised by the results?

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Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

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Draw some angles inside a rectangle. What do you notice? Can you prove it?

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Can you work out the fraction of the original triangle that is covered by the inner triangle?

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Do you have enough information to work out the area of the shaded quadrilateral?

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Can you work out the fraction of the original triangle that is covered by the green triangle?

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