We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
230
1
avatar

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?

 Jul 6, 2018
 #1
avatar
+1

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.

 Jul 6, 2018

12 Online Users