2022 SSMO Speed Round Problems/Problem 2
Problem
A bag is big enough to hold exactly 6 large pencils, 12 medium pencils, or 30 small pencils, with no space left over. Given that there is 1 large pencil and 3 medium pencils currently in the bag, what is the maximum number of small pencils that may be added to the bag? Note that there may still be space left over in the bag.
Solution
Each large pencil takes up 
th of the bag, each medium pencil takes up 
th of the bag, and each small pencil takes up 
th of the bag. So, our answer is ![\[\left\lfloor\frac{1-\frac16-3\cdot\frac1{12}}{\frac1{30}}\right\rfloor=\left\lfloor\frac{\frac7{12}}{\frac1{30}}\right\rfloor=\left\lfloor17.5\right\rfloor=\boxed{17}.\]](http://latex.artofproblemsolving.com/9/c/c/9cc8a3877cf2f8fb869649ab9f297c8eabff8b4f.png)
~pinkpig
