Math CentralQuandaries & Queries


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.


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!


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