At a tender age my father introduced me to an arithmetic game: making the number 11 from five single digits using only the basic operators listed here:
+ addition - subtraction * multiplication / division ^ exponentiation () parenthesis ! factorial SQRT() square root SQ() square (written in 1930's Netherlands using a small *square* as exponent)
The challenge is to construct an expression with value 11 ten times, each time using exactly five instances of a single digit from 0 to 9.
11 = (4 + 4 + 4) - (4 / 4)
is a correct solution for five 4's.
You are tasked with posing a solution for all 9 remaining combinations of five identical digits. One is much more challenging to solve than the others, but I will leave that to readers to identify. Solutions for all ten cases of five identical digits are known to exist.
Back when Ontario car licence plates were two letters and five digits, the challenge for a ten year old was to solve each such puzzle before another car came into view.