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?

Guest Mar 26, 2020

#2**+1 **

**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?**

\(\begin{array}{|rcll|} \hline \text{eggs}_{\text{min.}} &=& 1+lcm(12,13)*n \qquad n\in \mathbb{N} \\ \text{eggs}_{\text{min.}} &=& 1+12*13*n \\ \text{eggs}_{\text{min.}} &=& 1+156*n \quad | \quad \text{eggs}_{\text{min.}} \mathbf{\geq 200 !},\ \text{so } n=2 \\ \text{eggs}_{\text{min.}} &=& 1+156* 2 \\ \mathbf{\text{eggs}_{\text{min.}}} &=& \mathbf{313} \\ \hline \end{array}\)

heureka Mar 26, 2020