$$31$$ children stand in a row from the shortest to the tallest. The last child is $$131$$ cm height. Tom stands the $${{10}^{\text{th}}}$$ place counting from the first. No two children have the same height. What is the maximum heights of Tom? (The height of all the children are whole numbers.) 
Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Extreme Value in Inclusion-Exclusion for Multi-sets