1.) 3 a.m. describes an event occurring 8 hours after 8:00. It must be talking about 8 a.m. or it would be the next day. Therefore 8 a.m. is eat and 4 p.m. is sleep.
2.) 4 p.m. tells you that 1 p.m. is play.
2.) 8 a.m. tells you that Titan ate at night (bottom row). 4 p.m. tells you that 5 hours after every eat is a play. The only way for Titan to have eaten at night and still played five hours later is if 6 p.m. is eat and 11 p.m. is play.
3.) According to 1 p.m. and 6 p.m., Titan must have had exactly four walks (5 hours apart) six walks (3 hours apart), or fifteen walks (1 hour apart). No other amount of walks would allow equal time in between except two, but 6 p.m. says Titan had at least three walks. Basically, the only factors of 15 are 1,3,5, and 15. Fifteen walks clearly does not work, because they would all have to be consecutive, and they can’t be since too many time slots are already filled in. Also, there is no way to make six walks work. At three hours apart, one of the walks would coincide with another already filled in activity, no matter which of the four remaining night time slots the last walk would be. So you know that Titan had four walks, and so they are 5 hours apart each. Since the last walk is at night, you can trace the four possible solutions and rule out any that have filled in time slots. What you find is that 7 p.m., 8 p.m., and 10 p.m. could all be the final walk, but 9 p.m. could not. This is because the second last walk would then have to be at 4 p.m., which is already filled in with sleep. This means that any time slot on this path cannot be a walk, including 11 a.m. In addition, 11 p.m. tells you that 11 a.m. is also not eat or mischief. 3 a.m. tells you that 11 a.m. is not sleep. Therefore 11 a.m. must be play.
4.) According to 1 p.m. the first walk is no earlier than 4.a.m. So 12 a.m. is not walk. 12 a.m. is also not eat or mischief according to 11 p.m. And 12 a.m. is also not sleep according to 11 a.m. Therefore 12 a.m. must be play.
5.) You know from 1 p.m. and 6 p.m. that the last walk is 7 p.m., 8 p.m. or 10 p.m. That means there is also a walk at 2 p.m., 3 p.m., or 5 p.m. Therefore the only place for Titan to have slept four consecutive hours is somewhere between (and including) 1 a.m. and 7 a.m. There are many scenarios as to which four or five or six of those hours is sleep, but in all of them, 4 a.m. is one of them. Therefore 4 a.m. is sleep
6.) Looking at 4 a.m. you know that it’s not 5:00 and 10:00 because of 11 p.m. So Titan definitely got into mischief at 3:00 and 7:00. 3 a.m. is already filled in; therefore 3 p.m. is mischief.
7.) 4 a.m. being filled in ruled out 7 p.m. as the last walk. 3 p.m. being filled in rules out 8 p.m. as the last walk. 9 p.m. was ruled out long ago, with 4 p.m. being filled in early. Therefore the last walk, according to 1 p.m. and 6 p.m., is 10 p.m.
8.) With 10 p.m. as the last walk, the other three fall into place at 5 p.m., 12 p.m., and 7 a.m.
9.) You could have gotten 7 p.m. before step 7 because placing the second mischief at 7 a.m. would have killed any chance of placing four walks 5 hours apart each, but in any case, now it’s very obvious that the second mischief is at 7 p.m., according to 4 a.m.
10.) All the walks are now known. According to 4 p.m., 2 p.m. is not eat, since 7 p.m. is not play. Therefore, according to 5 p.m., 2 p.m. is play.
11.) According to 8 a.m., 2 a.m. must be sleep.
12.) 2 a.m. refers to 11 a.m.-12 p.m. Therefore all other walks are immediately preceded by sleep. Therefore 6 a.m. and 9 p.m. are sleep.
13.) According to 9 p.m., 5 a.m. must be sleep.
14.) According to 5 a.m., 8 p.m. must be play.
15.) 8 p.m. refers to 1-2 p.m. Therefore 10 a.m. is not play. All the walks and mischiefs are known and according to 4 or 11 p.m., 10 a.m. cannot be eat. Therefore 10 a.m. is sleep.
16.) 10 a.m. tells you that both 1 a.m. and 9 a.m. are eat or sleep. According to 4 p.m., 1 a.m. cannot be eat, so it must be sleep.
17.) According to 1 a.m., all eats are already known; therefore 9 a.m. is sleep.