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MATH / Let an integer x be bad if there is no way to insert a colon among the digits of x to form a time of day (on a twelve-hour, digital clock), and good if a colon can be inserted to f…

Problem

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problem

Let an integer xx be bad if there is no way to insert a colon among the digits of xx to form a time of day (on a twelve-hour, digital clock), and good if a colon can be inserted to form a time. For example, 100 is good because we can write 1:00, but 164 is bad. How many bad integers between 100 and 200 are equivalent to 3 mod 4?
Plain-text mathematical notation (without MathML)
Let an integer x be bad if there is no way to insert a colon among the digits of x to form a time of day (on a twelve-hour, digital clock), and good if a colon can be inserted to form a time. For example, 100 is good because we can write 1:00, but 164 is bad. How many bad integers between 100 and 200 are equivalent to 3 mod 4?
Original LaTeX notation
Let an integer $x$ be bad if there is no way to insert a colon among the digits of $x$ to form a time of day (on a twelve-hour, digital clock), and good if a colon can be inserted to form a time. For example, 100 is good because we can write 1:00, but 164 is bad. How many bad integers between 100 and 200 are equivalent to 3 mod 4?

level

Level 4

type

Number Theory

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Source and history

task_id
def0794f-e2b8-5e3c-970a-8515d5ec85b0
task_key
number~5ftheory--test--def0794f-e2b8-5e3c-970a-8515d5ec85b0
task_revision_id
1
config / split
number_theory / test

Official source

initial import