



 
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!
 


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 