It’s midnight.
A hardworking Miss Loi remained behind at The Temple to mark her student’s homework diligently, even as the last glow had long faded from the dying cinders of joss sticks in the area.
The silence was deafening, since the last noisy Jφss Sticks session ended hours ago, and no getai has ever been held to ruffle the eerie tranquility of Novena during certain times of the year.
A sudden cold chill swept through the air, as the sound of someone knocking on the Temple Gates unsettled the deathly stillness of this moonless night.
Verifying that she didn’t accidentally lower the environmentally-friendly 25° temperature of her aircon, Miss Loi went outside the room to find a tall, expressionless man at her doorway, dressed in traditional Chinese costume.
Wah! You just come from the Beijing Olympics Opening Ceremony or did NDP ended late? Can I help you Sir?
asked Miss Loi.
I need mathematics tuition.
replied the man in a soulless voice.
Which level are you? When are you available for tuition?
I take Imperial Examination. Only available 12-6am.
Errr … sorry we’re closed during those hours and … umm … how old are you?
Next week my 300th birthday. Must pass Imperial Exam. Must have tuition! MUST HAVE MISS LOI!
With that, the man raised his arms outwards and started hopping menacingly towards a terrified Miss Loi.
While retreating, Miss Loi quickly whipped out her ancient Nokia N73 to call a friend who happens to be moonlighting as a temple medium:
HELP! I’M BEING ATTACKED BY A 僵屍! HOW?!
After a brief moment, came this reply:
天灵灵地灵灵 …
Each term in the expansion of 
represents each of the n hops that the 僵屍 makes.
Given that the fifth term is independent of x, you must write the coefficient of the middle term on a piece of yellow paper and paste it on his forehead in order to stop the 僵屍.
Luckily, a stack of bright kawaii yellow Post-It notes lay within reach on Miss Loi’s desk. Now all she needs is the value of that coefficient.
Having just taught a class on Binomial Theorem, she recalled that it’s a pretty straightforward topic with questions that should easily be done in 10-15 minutes to bag your 6-8 marks (provided you can recall the two formulae corresponding to generally two kinds of questions for this topic:
- The ones that require you to expand an expression.
Or the kinds (like this question) that require you to find a specific term and/or its coefficient in an expansion, utilizing heavily the following formula:
In the expansion of (a + b)2, the (r+1)th term:Tr+1 = nCr an–rbr
*Note that the Binomial Coefficient nCr can be denoted by
So unless you’re attempting this question alone in the middle of the night, it should be easy for you to find the coefficient before the 僵屍 grabs Miss Loi by the neck and drags her to the netherworld to conduct maths tuition!
N.B. Some of you should find this question familiar 😉
