Tip: the Sodner's constant is the unique positive root of the Logarithmic integral function.
This problem needs a better description. For instance, it is not clear why arithmetic is banned, after all any function uses it and it is really easy to hide the constant's value within non conventional operations (the leading solution did exactly that). It would probably be best to just force the player to use some function or to suggest what kind of solution is expected.
Thanks for the suggestion, Rafael. I edited the description. I appreciate that James also submitted a solution demonstrating understanding of the definition of Soldner's constant.
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