Puzzles | Arithmetical puzzles | Four 4's equal...

Use exactly four 4's to form every integer from 1 to 50, using only the operators '${\displaystyle +}$', '${\displaystyle -}$', '${\displaystyle \times }$', '${\displaystyle /}$', '()' (brackets) ${\displaystyle x^{2}}$ (square), and '!' (factorial). The square and factorial operators should be used as sparingly as possible. If 44 (which is 4 x 10 + 4) can be avoided, avoid it. In this version of the problem, the square root operator is not allowed.

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