其它
Allen has some apples, and the number of apples is more than $2200$ but less than $2300$. If he distributes them among $12$ children evenly, there will be $11$ apples left. If he distributes them among $13$ children evenly, there will be $7$ apples left.~ If he distributes them among $14$ children evenly, there will be $3$ apples left. Which is the correct range of the number of pens? 
Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem
If he distributes them among $12$ children evenly, there will be $11+12\times4=59$ apples left. If he distributes them among $13$ children evenly, there will be $7+13\times4=59$ apples left.~ If he distributes them among $14$ children evenly, there will be $3+14\times 4=59$ apples left. So at least he takes $59+12\times 13\times 14=2243$. 