"Sir, why do we use letters?"

There is something unusual about the answer to the ultimate question of life, the universe and everything:

Think of a number, any number. Add seven to that number, and multiply your answer by three. Subtract nine from that number, and double your answer. Add 228 to you answer and then divide that number by six. Finally, subtract the number you started with. What number are you left with?

Magic. At least enough to give me a good trial for witchcraft given the correct temporal context. But it only stays magic in the world of arithmetic, which is enough to baffle both my class (and possibly a reasonable number of adults) with a "how did he do that?" variety of wonder.

If we satisfy ourselves with just picking a number and trying to work through my problem over and over again, we will be left bewildered by why we get the same answer every time, no matter what number we pick originally. This is why we need to use letters, or algebra - the only way we will ever see what is going on is if we somehow do this problem for every number in existence simultaneously. This particular problem is nice because there is an initial shock when it first works, and somewhat impenetrable without generalising, but falls apart with a small amount of algebra:

Think of a number - x
Add seven - x + 7
Multiply by three - 3(x + 7) = 3x + 21
Subtract nine - 3x + 12
Double answer - 2(3x + 12) = 6x + 24
Add 228 - 6x + 252
Divide by six - x + 42
Subtract your original number - 42

I will concede that one disadvantage is that this feels like "unweaving the rainbow", there's a certain amount of fun in the "magic" that's a shame to lose, but it's a nice demonstration of why we do need to use letters rather than numbers some of the time.

Editted as there was a, ahem, 'deliberate' mistake. Once it was spotted, it would have of course been misleading to keep it there...