Your friend has an egg collection comprising at least 200 eggs. He wants to store them in dozen-egg containers. After filling as many containers as possible, the last container had 1 egg left over. He then decided to store his eggs in customized baker-dozen-egg containers, where each container can hold 13 eggs. It turns out that, after filling as many of these containers as possible, he still has 1 egg left over. What is the minimum number of eggs that your friend could have?
Your friend has an egg collection comprising at least 200 eggs.
He wants to store them in dozen-egg containers.
After filling as many containers as possible, the last container had 1 egg left over.
He then decided to store his eggs in customized baker-dozen-egg containers, where each container can hold 13 eggs.
It turns out that, after filling as many of these containers as possible, he still has 1 egg left over.
What is the minimum number of eggs that your friend could have?
\(\begin{array}{|rcll|} \hline \text{eggs}_{\text{min.}} &=& 1+lcm(12,13)*n \qquad n\in \mathbb{N} \\ \text{eggs}_{\text{min.}} &=& 1+12*13*n \\ \text{eggs}_{\text{min.}} &=& 1+156*n \quad | \quad \text{eggs}_{\text{min.}} \mathbf{\geq 200 !},\ \text{so } n=2 \\ \text{eggs}_{\text{min.}} &=& 1+156* 2 \\ \mathbf{\text{eggs}_{\text{min.}}} &=& \mathbf{313} \\ \hline \end{array}\)