[math-fun] Imbalance

Hello Math-Fun, In this country, digits go by closed boxes containing 10 distinct digits each. To write the number 2019 you can open a single box and extract the digits 2, 0, 1 and 9. We call "imbalance" the quantity of unused digit in one (or more) opened box(es). So, writing 2019 leaves an imbalance of 6 (the 6 unused digits in the box). Now, if we want to write 2020 we must open two boxes (...) The question: "Is S infinite?" is explained there, on my personal blog page: http://cinquantesignes.blogspot.com/2020/02/integer-imbalance.html Best, É.