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(12/06) Moe Michaels: Start by separating the shurikens into four piles of 5, we'll call these piles 1, 2, 3, and 4.
1st move, take piles 1 and 2 and put them on the balancing scale.If pile 1 weighs more or less then pile 2, put pile 2 aside and compare 1 and 3. If pile 1 still weighs more or less then pile 3, the fake is in pile 1 (and from this we can see that the fake shuriken is heavier or lighter then the real ones), if they're even, the fake is in pile 2 (and the fake shuriken is again heavier or lighter), and the fourth doesnt need to come into play. If 1 and 2 are even, put one of them aside and compare with pile 3, if even again, then pile 4 has the fake(***), if 3 weighs more or less then 1 or 2, then 3 has the fake (and the fake shuriken weighs more or less then the real ones).
This takes 2 steps and determines which pile of 5 has the fake and also allows you to figure out whether the fake shuriken weighs more or less then the real ones.
Last 2 moves....
split the pile of 5 into 2 piles of 2 and 1 left over. Balance the 2 piles, if you get lucky enough and they weigh the same, you've found the fake in 3 moves because the leftover shuriken is the fake.If pile one weighs more then pile 2, or if pile 2 weighs more then pile 1, knowing whether the fake shuriken weighs more or less then the real ones, you can determine which pile of 2 has the fake, and from there balance the 2 shuriken of the pile and there you will find your fake.
(***)The only problem with this solution is that you dont know whether the fake shuriken weighs more or less then the real ones, and to determine the fake one it could possibly take an extra fifth step.
Shika: Nope. It's possible to find out in 4 steps. Try again!
(12/06) Jonny : Hope i can put this to words in english (reading and unndertanding are easy to m, but writing... ok, maybe i'll just make some pics to explain wht I mean.
Method 1: Balancing system.
1st step:put half of the shurikens on the one side of the balancing system, the remaining ten on the other. The system won't be balanced, of course, since one of thoose shuriken has a small difference in wieght then the others.
2nd step: take away one shuriken from each side. When the system is balanced, it means one of last two shuriken u took away was the fake one. Now have to find out wich one is the fake.
3rd step: U now need the 2 shuriken you just took apart. Get a third shuriken, and place it on one side of the balancing system. now place one of the two 'chosen' shurikens (one of wich is the fake u don't know yet) on the other side. Unless the vendor sold you 2 fake shurikens and u got a very bad luck, u now know the truth.
If the system is perfectly balanced, the two balancing shuriken are both real ones and the one u keep in yuor hand is the fake. otherwise the system will bei, even if only slighhtly, unbalanced, so the last shuriken you placed is the fake one.
4th step: beaut up the vendor and get other 20(real) shurikens for free.
Method 2: Water (or oil) test
This one is a 1-step way to find out the fake, but it's reccomended to grease the shurikens before u do this, and after u have to clean em up and grease them again (or they'r goin' to rustin no time).
Just fill a transparent recipient with a liquid substance with some density (oil may be good)
now u just got to observe wich shuriken sinks at visibly diferent speed (the higher the liquid's density, the greater the difference) It may take some trials to do that, so it' s not that useful.
Method 3: Water test again
Just ask for a washcup, or something like that, full of water, and be sure you got something plain that floats on water (even if u put a shuriken on that plain object. I'll call it a float from now on). Make sure the water almost drips out of it's cntainer, carefully place your float on the water. Be sure the water won't make any significant waves, or you may have to start over. Thoose of you good at physics (ehr... i never was good at it) will now surely know what comes. We use the Archimedes Rule (it's called that way in english ? dunno..). I'll try to explain it the complex way.
with the water level right to the borders of the cup, when we put a shuriken on the float, some water will drip out. if we now take away the shuriken again, te water level will be under the cup's borders. Now we place another shuriken un the float. Water level will, if this shuriken has same weight than the first one, raise till the borders, but will not drip out. repeat placing shurikens till u get one of thoose situations: water drips out, or the water level won't reach the borders of the cup. Congratrulations, u have found the fake shuriken. Even if the first one was the fake you will know it, because the water level will be identtical the 2nd and 3rd time.
But why do we use the float? That is for the archimedes rule. Being the fake and real shuriken the same dimentions, they would move an identical amount of water, so there would not be any difference in water levels for the both kind of shuriken. We know the fake shuriken feels and looks like a real one, so we can assume that they have exact idetic volumes. But since there is a slight weight difference, it means the fake's density is not the same as the real ones's. Placing them on an identical float will make the difference of weight decisive: the amount of water moved will be related to the compound density of both the float and the shuriken on it. so if we have a heavyer shuriken on the same float, that will move more water then with a lighter shuriken.
Well... sorry for my bad english. If u understood even only partially anything i wrote here, let me kno. If not... ask your physics or maths teacher, they surely will understand it easier. And if they don't understand... I'm really sorry.
Shika: Don't get so carried away. I said 4 steps involving the beam balancing scales. What's with the oil and water?? Your Method 1 exceeded 4 steps as well. By 4 steps, that means you're only allowed to place the shurikens on the balancing scale 4 times. My physics and maths senseis have a lower IQ than me and would have hurled the duster at the explanation. Next!
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