其它
When Ringo places his marbles into bags with $6$ marbles per bag, he has $4$ marbles left over. When Paul does the same with his marbles, he has $3$ marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with $6$ marbles per bag. How many marbles will be leftover? (2012 AMC 10B Problems, Question \#4) 
Overseas Competition->Knowledge Point->Number Theory Modules
In total, there were $3+4=7$ marbles left from both Ringo and Paul.We know that $7 \equiv 1(\bmod 6)$. This means that there would be $1$ marble leftover. 