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Let an integer  be bad if there is no way to insert a colon among the digits of  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 5?

 Nov 26, 2020
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How many bad integers between 100 and 200 are equivalent to 3 mod 5?

 

103  108  113  118  123  128  133  138  143  148  153  158  163  168  173  178  183  188  193  198  Total = 20 integers.

 Nov 26, 2020

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