Granny has $$10$$ grandchildren. Alice is the oldest. One day, Granny notices that her grandchildren all have different ages. If the sum of her grandchildren\textquotesingle s ages is $$180$$, what is the youngest age that Alice can be． 
Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums
Try to consider the problem of the youngest Alice in such way: make each grandchild has a similar age as possible, and the age of each grandchild should be different, that is, $$1 + 2 + 3 +\cdots 9 + 10 = 55$$; then $$180 - 55 = 125$$, $$125 \div 10 = 12\cdots\cdots5$$, and $$5$$ is left. If every child\textquotesingle s age is added by $$12$$, then $$5$$ is left. Give the extra year to each of the $$5$$ children who are the oldest. In doing so, the minimum number of Alice\textquotesingle s age is $$10+12+1=23$$. 