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MATH / A Chinese emperor orders a regiment of soldiers in his palace to divide into…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A Chinese emperor orders a regiment of soldiers in his palace to divide into groups of 44. They do so successfully. He then orders them to divide into groups of 33, upon which 22 of them are left without a group. He then orders them to divide into groups of 1111, upon which 55 are left without a group. If the emperor estimates there are about two hundred soldiers in the regiment, what is the most likely number of soldiers in the regiment?
Plain-text mathematical notation (without MathML)
A Chinese emperor orders a regiment of soldiers in his palace to divide into groups of 4. They do so successfully. He then orders them to divide into groups of 3, upon which 2 of them are left without a group. He then orders them to divide into groups of 11, upon which 5 are left without a group. If the emperor estimates there are about two hundred soldiers in the regiment, what is the most likely number of soldiers in the regiment?
Original LaTeX notation
A Chinese emperor orders a regiment of soldiers in his palace to divide into groups of $4$. They do so successfully. He then orders them to divide into groups of $3$, upon which $2$ of them are left without a group. He then orders them to divide into groups of $11$, upon which $5$ are left without a group. If the emperor estimates there are about two hundred soldiers in the regiment, what is the most likely number of soldiers in the regiment?

level

Level 4

type

Number Theory

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Source and history

task_id
f3d19bf3-0313-503f-b6c4-e3dd3d0e4cd8
task_key
number~5ftheory--test--f3d19bf3-0313-503f-b6c4-e3dd3d0e4cd8
task_revision_id
1
config / split
number_theory / test

Official source

initial import