The Number Crunching Machine

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

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The Number Crunching Machine

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

Why do this problem?

This problem is an amusing and thought-provoking way of practising addition, subtraction, multiplication and division. The results are diverse enough to keep learners working for a considerable time and to encourage methodical working. This sheet might be helpful.

Key questions

What operation do you need to do next?

Would it be a good idea to jot down your calculations as you go?

What numbers have you put in so far?

Have you made a list of the numbers you have already done?

How many numbers have you found that come out unchanged?

Possible extension

Learners could make their own number-crunching machine and try it out on their friends.

Possible support

Suggest trying with different numbers below $50$. It may help to make a version going across the page with arrows or you could use this sheet.