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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?

 Mar 26, 2020
 #1
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LCM of [12, 13] = 156

 

156 + 1 = 157 minimum number of eggs.

 Mar 26, 2020
 #2
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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?

 

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

 

laugh

 Mar 26, 2020
edited by heureka  Mar 26, 2020

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