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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?

Guest Jul 6, 2018
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N mod 4 =3, solve for N

 

N=4A + 3, where A =40 to 49 inclusive.

49 - 40 + 1 =10 "bad" integers between 100 and 200 as follows:

163, 167, 171, 175, 179, 183, 187, 191, 195, 199.

Guest Jul 6, 2018

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