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MATH / 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…

Problem

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problem

Your friend has an egg collection comprising at least 200200 eggs. He wants to store them in dozen-egg containers. After filling as many containers as possible, the last container had 11 egg left over. He then decided to store his eggs in customized baker-dozen-egg containers, where each container can hold 1313 eggs. It turns out that, after filling as many of these containers as possible, he still has 11 egg left over. What is the minimum number of eggs that your friend could have?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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?

level

Level 3

type

Number Theory

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Source and history

task_id
dbc4d3e3-9e30-5168-bdf8-0877168ec9fb
task_key
number~5ftheory--test--dbc4d3e3-9e30-5168-bdf8-0877168ec9fb
task_revision_id
1
config / split
number_theory / test

Official source

initial import