Expressing the natural numbers in terms of 4 fours. If you allow all standard math operations (say those covered by a normal high school science math course) there is an algorithm that, for any natural number, constructs an expression for it using four fours. This has been known for some time & frequently rediscovered. Can you find it? Hint: For any N, there are only finitely many formulae using four fours and N operations. Thus most of the expressions must use huge numbers of operations with at most four numbers. What does this tell us about the operations that will be used? Good Hunting! RD

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Question from Steve:

When I was studying mathematics, there were several of us that tried to express the natural numbers in terms of 4 fours. Allowing the use of any known math operation, for example n to the zeroth power is 1.Is there more info on this exercise. This was done mentally, nothing written down.

Steve,

If you allow all standard math operations (say those covered by a normal high school science math course) there is an algorithm that, for any natural number, constructs an expression for it using four fours. This has been known for some time & frequently rediscovered.

Can you find it? Hint: For any N, there are only finitely many formulae using four fours and N operations. Thus most of the expressions must use huge numbers of operations with at most four numbers. What does this tell us about the operations that will be used?

Good Hunting!
RD

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