At my office we lost a lot of time because someone put up a challenge to represent all the numbers 0-99 with algebriac expressions containing exactly four digits '4'. The use of powers and radicals was allowed.<p>I myself solved several numbers before exhausting the tricks I could think of, and reverted to brute force/search with Polish/prefix notation, then realizing how massive the search space was for even just a few operators. Adding parentheses ordering further explodes the search space.<p>Finally, while this kind of concrete and explicit expression is "toy math", it is related to Godel Sentences and lexigraphic ordering of proofs used through much of the establishment of logic, the foundations of proof systems, and computer science.