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4444

A few weeks ago the “four fours” puzzle appeared on a whiteboard at work. (Construct natural numbers from four “4” numerals and some reasonable set of mathematical operators.)

There are plenty of solutions online - I recommend this answer key. However, I found I disagreed a bit with author David Wheeler’s aesthetics of purity. I prefer allowing the percentage symbol to the Gamma function, and I also tweaked my search algorithm to reward symmetry and brevity.

So here is my own little collection of 4^4 solutions, in MathML and ascii forms. (The only construct you may not immediately recognize is “.4” with an overline to indicate nought point four recurring, which evaluates to four-ninths.)

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