You are given 6 balls and a weighing scale. 2 balls are defective and they weigh less than the other 4. You are only given 2 weighs (you can only use the scale twice; taking off the balls don't count). Find out which are the defective balls.
Remember, it's TWO defective balls, no typo.
Aaaaaaaand I've got great news for you, reader! I'm going to reveal the answer to this puzzle!!
Warning: If you're not really into abstract thinking, be prepared to get really lost in your thoughts....
(Press the "read more" button at the bottom of the post).
The first step you must take is to put 3 balls on each side of the scale. You might be faced with 2 scenarios, as the scale can either be imbalanced or balanced. I will start with the imbalanced scale first. I'll number the steps to prove that it can be done in two weighs (2 steps; you can use the scale twice), and so you know what's going on.
Imbalancedor Scenario 1
This tells you one thing: both defective balls have to be on the same side, otherwise it would appear as a balanced scale (one on each side).
1. Your first step (as shown above) would be to put 3 balls on each side of the scale. If it turns out imbalanced, remove all 3 balls on the heavier side, because you can bet on your life that there are no defective balls there.
2. Move one ball to the empty side (you removed 3 balls from there in the first step), hold one in your hand, and leave one the scale untouched. [If you're following the illustration above, move the black (shaded) ball over the empty side, hold the peach ball and leave the unshaded one where it is.]
Balanced: Both balls are on the scale
Imbalanced: The one on the lighter end of the scale is defective. The other one is in your hand.
There! The first scenario completed!!
And things get really messy now........refer to the diagrams as often as possible to avoid getting confused.
Balanced
This type means that there is one defective ball on each side of the scale.
1. Remove one ball from each side.
There are two possibilities after step one: the scale can either stay balanced or become imbalanced. I'll tackle the balanced one first.
Scenario 2(a)
Balanced = Both defective balls have to be EITHER
a) One on each scale
b) Both removed, and are on the ground now
Step 2(a): Switch ONE ball from ONLY ONE side of the scale. [Illustration: Switch the blue ball on the scale with the blue ball on the ground.]
After switch
2. Imbalanced (the side you switched got LIGHTER): You replaced a normal ball for a defective one. BOTH DEFECTIVES WERE ON THE GROUND. Story ends here for this scenario.
2(a) Imbalanced (the side you switched got heavier): You switched the defective ball with a normal one. The pink one is normal.
2(a) Balanced : Defective ball is pink.
[How do I know?? Because both defectives have to either be on each scale OR both on the ground.
1. If both were on the ground, the scale would have become imbalanced right after swapping the blue balls, because that's what happens when you switch a heavier ball with a lighter one.
If the ball you swapped was defective itself, then BOTH defectives MUST have been on the scale (one on the other side) and the 2 balls on the ground MUST be normal. You would have caused the scale to become unbalanced, because that's what happens if you swap a lighter ball for a heavier one.] More on this in scenario 2(b).
Still in step 2(a): You now know the type/condition of at least ONE ball from ONE side. In every scenario (except the one where "the story ended"), remove ONE BALL FROM EACH SIDE to find the other side's defective. Please rely on your imagination and common sense for this one.
(Eg: Remove the defective and another ball from the other side. If the scale is balanced, you know that you're holding both defectives. If scale is unbalanced, you're not stupid enough to not be able to tell which side is heavier or lighter.)
Scenario 2(b) [right afterstep 1]
The scale became imbalanced because the type of balls you swapped were different from those on the ground. Whatever the case, the lighter side has one defective, the heavier side has 2 normals. Remember, both defectives CANNOT be on the lighter side or you would've got scenario 1.
Step 2(b): This step is NOT related to step 2(a), so no switching of balls is involved. Remove both on the heavier side and shift one over to the now empty side OR remove one ball from each side.
Ta-daaaahhh!!! Now I hope you were smart/not blur enough to digest all that. Happy moping.
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You know Pacific West? That company that sells seafood stuff (and advertises a lot)? Apparently the owner of that company is my father's best friend. (Now I know where to get free and good food)....
Awesome, right?!?! And he has my favourite breed of dog, imported from Australia, costing 5000 bucks each. Border collie, the smartest breed of dog, stays inside his gigantic house and runs up and down happily. And it seems that the Fuzzy's trainer got fed up of training it because it doesn't listen to him. Maybe Fuzzy only prefers to listen to its one and only family. But he was very friendly to my mum and I, allowing us to pet him. He was wary of my father, though, and kept barking at him.
At least Fuzzy isn't some jittery, hyperactive dog (like Silkie) or a Pitbull Terrier. I've found that Pitbull Terriers have been banned from Switzerland (or maybe the whole Europe?), as they're very strongly built and are aggressive. And once they get angry, the only that can stop them is a bullet. Then, they die and you find out that there's no point rearing them (you need to have a license to rear them anyway).
Back to Pacific West....no, we didn't get free food, but we DID get free lunch during some reunion among 5 long lost friends, including my father and the President of PW.
And we went into his house, wholly designed on the basics of Feng Shui. It was really nice and had an antique feel to it (there was a lot of wood). But my favourite part of the house was the dog running around us. *Grins*
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You would notice a "Read more" button below. Click it.
You've seen the magic before, so stop wasting your time!
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It's the new year!!! And I have a lot of things to say....or not. Well, the main thing is that school is getting annoying.
And so is blogging.
(That was anticlimactic, no?)
Fine, so school isn't really getting on my nerves. It's whatever that happens within school, concerning the junky homework plopped onto my desk everyday. And with people like me who are programmed differently, homework ranks very lowly on my list of priorities. And it doesn't help to note that all those on the same frequency as I am are leaving this accursed country and the screwed-up education system. Now I feel like I'm just some sad, lifeless zombie doing schoolwork day in, day out. I can't stand the prospect of looking back at my life 20 years later and saying, "Wow, I sure did a lot of homework last time!"....Of course, people call that nerdjobs, but I call it plain nutjob. Sometimes, I wonder why students don't just go all out in full force and not do homework. Come to think of it, if everyone including the good students don't do homework, it wouldn't actually be considered wrong to not do homework anymore, seeing that teachers trust good students a lot.
I'm talking too much nonsense, so enough of that....Happy Chinese New Year to all those who celebrate it. Mathematics is fun, but when you get tons of the same thing EVERYDAY, the excitement just wears off. So now, Maths is really dull. Batai won the interclass debate.....and there's nothing to blog about. Either that, or I'm simply too lazy to post anything up. Honestly, life isn't boring me yet, but coming up with something to entertain you guys is. So I'm going to stop here. And I expect you to stop here too and ogle my blog template.
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I know it's a fortnight late, but nevermind, I'll just summarize some key events that happened since New Year's eve, which I did not even elaborate on.
1 Jan '10, Fri
I finally did something I've always wanted to do : watch fireworks while listening to 1812 Overture. I got sick in the morning with a sore throat and a disobedient nose.
4 Jan, Mon
I've always had the premonition that I might go into 4 Batai, and I did--with all the other English freaks!!! Gheek, Shu Wen, Daniel, Tim, Mel, etc....sigh, all those smart people squeezed into one class. I was elected as class treasurer (and I think people actually regret it). All I do is terrorize the class and steal their money. I got 6 mosquito bites in Lab 2 alone....and I thought Mel was supposed to be the mosquito magnet. Got a random nosebleed without warning in choir later in the afternoon.
5 Jan, Tues
Found out about 4 Batai's special status. Apparently, there's a joke the teachers share among themselves; they call us "non-halal", because there are no Malays in our class at all. Of course, we students have jokes too, our specialty being the class monitor, Zhi Chung. All the teachers who taught our class made the same jokingly sarcastic comment, "Are you sure you chose the correct monitor?". Pn Sharon confessed that she's afraid to ask Zhi Chung to do anything, since he "always looks so sad". The irony was that she told us that after sending him off to get a pile of books for the class.
7 Jan, Thurs
Class collection since 6th Jan : RM1186
See what I meant by "I terrorize the class" now?
8 Jan, Fri
Signed up for all those crappy extra-curricular activities.
9 Jan, Sat
MWGC held their one-year late annual dinner. My father invited Mr Heng to go along.
12 Jan, Tues
Applied to enter prefecthood once more.
13 Jan, Wed
Aunt from Amsterdam came over.
14 Jan, Thurs
Had a very screwed up Nostalgia meeting, which ended with a freaky plot to cut our 2010 year short. Apparently, the Datin is leaving this July and would appreciate the production of the magazine to be done by July. In her masterplan, all the school events would be crammed between now and June; there would be nothing going on after that period, unless the new principal has something funny in mind.
15 Jan, Fri
Introduced the class accounts and money objectives.
Today: Teeth. Braces. Bite. Ouch. (You don't need elucidation on this one).
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