During the recent Chinese New Year house spring cleaning, Miss Loi stumbled upon a dusty old diary from years ago …
2 Jan 199X
Dear Diary,
This is my first entry.
I woke up at 6.30 AM today. I brushed my teeth at 6.36 AM. After that, I took my bath at 6.39 AM. After that, I ate breakfast at 6.47 AM. After that, I changed into my school uniform at 7.00 AM. After that, I went downstairs to the bus stop to wait for the bus. The bus arrived at 7.05 AM. After that …
*flips pages impatiently and fast-forward several years ahead*
6 Feb 199(X + 3)
Dear Diary,
Yeah! I scored full marks again for my math test today! Miss Lim even praised me in front of the class!
At the same time, she also scolded those who failed badly (it’s always the same few guys – one of whom is actually quite cute). She told them they are a disgrace to the school and asked them why can’t they just be like me and study like me.
Actually I hope Miss Lim would stop asking those guys to be like me, because every time she does that, the looks they (and some of my classmates) gave me are pretty scary.
OK I shall stop here – the TCS drama starring the handsome Li Nanxing is about to start soon!
9 Feb 199(X + 3)
Dear Diary,
You know Valentine’s Day is around the corner when all my classmates start to hao lian to me their plans for that night.
Anna is already getting all excited about her high class dinner at Jack’s Place. Sue is expecting nothing short of a big bouquet of roses containing the number of stalks symbolizing the number of days since she first met her stead.
As for me, while I would be VERY happy if HE (yeah one of the guys who always fails his math tests) asks me out on that day, I don’t think I’d stand a chance especially with this latest pimple outbreak.
Well time to study for the Math test which that sadistic Miss Lim had scheduled on 14 Feb.
10 Feb 199(X + 3)
Dear Diary,
HE smiled at me at the tuckshop today!!! I looked around just to confirm if HE wasn’t smiling at someone else behind me! I didn’t know how to react but I sure hope he doesn’t think I was acting dao.
Can’t sleep that’s why I’m writing this.
11 Feb 199(X + 3)
Dear Diary,
OMG HE smiled at me again today!!! I think I blushed till my pimples burst!
Die lah didn’t study much for the math test – all I can think of now are his beautiful eyes and his captivating smile …
12 Feb 199(X + 3)
Dear Diary,
You can’t imagine what a life-changing day it’s been! HE APPROACHED ME AT THE TUCKSHOP AND ASKED ME TO BE HIS VALENTINE!!!
Of course I said yes! Can’t wait to tell Anna and Sue about this!
Will go to B B Fashion after school tomorrow to shop for a new dress!
13 Feb 199(X + 3)
Dear Diary,
Something terrible has happened.
As HE has been failing all his math tests so far, HE told me that Miss Lim has warned him and his parents that tomorrow’s math test is his last chance to stay in our school. If HE fails it he’ll get kicked out of school immediately and our Valentine’s date would be off since HE will most likely be grounded by HIS parents.
HE suggested that the only way he could possibly pass the test would be for me to somehow smuggle my answers to him during the test.
I told him that’s cheating, but I realized it’s either that or no Valentine’s date for us.
Should I help him or not? Oh I’m so torn and confused!
14 Feb 199(X + 3)
Dear Diary,
It’s Valentine’s Day. It’s also the day of the dreaded math test.
Due to previous incidents of copying, Miss Lim has split the class into separate small rooms of nine students for this test.
As fate would have it, I’m seated directly behind HIM! As I usually finish each test with at least 20 minutes to spare, there should be enough time for me to pass my answers to HIM to copy and then get them back from HIM at the end of the test.
The diagram shows the seating arrangement during the math test. Miss Lim invigilates by patrolling VERY quickly in a general direction from the front to the back of the room.
The only way Miss Lim can spot me passing my answers to HIM (and vice versa) is when she is at the red shaded area in the diagram.
Those rounds when she walks from the back to the front of the room are not considered as it’s too dangerous to pass my answers around when we can’t see her.
Based on my past observations of the paths Miss Lim took in each round of patrol:
- When starting from the front of the room, the probability that she takes the path on her left is 0.6.
- At NO point will she travel in the direction back towards the front of the room.
- Whenever she reaches a junction, she NEVER turns toward the direction which immediately ends with a door.
- During each patrol, she NEVER revisits any portion of the path she has already walked EXCEPT when she reaches a dead end, where she turns back along the same path until she reaches the next junction.
Whenever she reaches a junction,
- the probability of her going straight is 0.3, and the probability of her turning left is 0.4, if she is free from all restrictions described in 2, 3, 4.
- the probability of her going straight is 0.6, if she is limited by any of the restrictions imposed in 2, 3, 4.
Given that I only have one attempt (right at the start of Miss Lim’s round) to pass HIM my answers, and that HE only has one similar attempt to pass them back to me once HE’s done copying, what’s the probability of either of us getting caught by Miss Lim?
Oh Diary I’m trembling with fear! Please, please let me know my chances of going for my first ever Valentine’s date tonight!
I’ve already bought that dress from B B Fashion. I’ve used up all my pimple cream. I’m DESPERATE!
P.S. Admittedly this question can be a little tedious – hopefully it can help members of the Lonely Hearts Club to pass some time on 14 February 😛
