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'The Number Crunching Machine' printed from http://nrich.maths.org/

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Put a number at the top of the machine and collect a number at the bottom.

What do you get?

Which numbers get back to themselves?

perform operations as follows: add 5, multiply by 3, if even subtract 2 or if odd subtract 1, multiply by 5, divide by 10, if odd add 3 and halve result or if even halve then if that result is even halve again or add 2 if result is odd