They found his diary under his bed.

Sherlock had been missing for three days now. His parents were in full panic ever since his missing was reported by his roommate. Mycroft had gone to the dorm and looked through his brother's possessions. He found the usual: notes of a true chemist, banned substances – he hid the latter in his pockets. He also found Sherlock's diary. Sherlock doesn't seem like the type to keep a diary. The truth is, he isn't. But Mycroft had asked him one day, after Sherlock had suffered a bad trip from marihuana, to write down what went through his teen mind. Maybe then they could identify why he turned to drugs, even if Sherlock insisted that it was mainly for science, concentration, or even fun.

Mycroft sat on the edge of Sherlock's bed and sighed before he opened the notebook. He hadn't actually ever read from it before. The first page was empty. The second page was a sort of title page.

'Sherlock's mind – letters to Mycroft'

Mycroft frowned. He hadn't expected his brother to write him letters. He flipped the page.

'34 days after the incident.

Dear Mycroft,

I've used cocaine today. Maybe too much. Maybe it was 7%, give or take.
Maybe give. As expected, nothing triggered it. I've passed the latest two
exams, the experiment I performed roughly two weeks ago succeeded, and
I have handed in the report. I expected a full score. I've not passed out after
taking it. And yes, I cleaned the syringe properly. No list needed, since
everything went as expected. "Had a blast," as my peers would probably
say. Now that I had a few hours of unlimited focus, I've been thinking
about the Postman Manor murder. Something doesn't add up. The media
get informed too much. The police can no longer trap suspects in hearings.
Everyone now knows the murder weapon, the location, the state in which
the victim was found. Perhaps if I solve this one, the police won't suspect
me this time. It seems like a safe case, doesn't it? He murder weapon was
the fireplace poker. Since there is only one fireplace (there is only one
chimney), the person must've known its location. We know the murder
happened in a mere five minutes. Also, the fireplace is located in a hidden
study, of which the police has not disclosed the location. It must have been
someone who knew the victim and the very secrets of the house. Tomorrow
I will be going to the police station to pick up a copy of the report. I'll let
you know my new discoveries then.

Sherlock'

Mycroft flips the page to see the next day.

'35 days after the incident.

Dear Mycroft,

The report states that the victim had no burns. Therefore, the fireplace
poker has been pierced through him cold. While we must not
underestimate their strength, the possibility that this has been done by
a woman is small. The angle of impalement is skewed to the right. Thus
we can conclude that the murderer is left-handed (the attack came from
the left side of the attacker, and to pierce the poker through the way it has
been, the poker was pointed slightly to the right). I have been to the Manor,
but I have been told by the butler that none of the residents currently live
in the Manor. He wrote down the address for me. I shall visit it tomorrow.
Are you thinking with me, Mycroft?

Sherlock'

Mycroft was thinking, but not about the case.
"Where are you, brother-mine?"
He wanted to skip pages, but he also felt obliged to read the rest. After all, it was clear that his brother expected him to do so.

'36 days after the incident.

Dear Mycroft,

I have visited the residents of the Manor, and they have informed me
– and proven to me – that none of them are left-handed. Now, I did
omit some information, but by now, I expect you to have your suspect.
I am informing the police tomorrow.

Sherlock'

'37 days after the incident.

Dear Mycroft,

The police have arrested the butler, and he has confessed. Another
case solved. Now tell me again that nothing good can come from
cocaine.

Sherlock'

Mycroft closed the notebook. His brother had been busy, apparently. But if this started 34 days after that bad trip, all of this must be from a long time ago. He hadn't thought his brother would actually keep some sort of diary, but he had done so. In his own way, of course.

Mycroft quickly flips through the pages. The notebook seemed filled for 90%; many more letters to come.