Re: [Pulze] The Weighing game, 13 COINS ?

> From: "Do / Ngoc Minh (ISE)" <n.do@student.canberra.edu.au>
> Subject: [Pulze] The Weighing game
> Dear pulze lovers,
> 
> I know another interesting pulze.  Hope you will like it.
> Minh.
> 
> -------------------------------------------------------------------------
> You have 12 coins, labelled A, B, ..., L. One of them is a fake. It is a 
> different weight to the others.
> You also have a pair of scales which you can use to weigh coins against 
> other coins. You are permitted 3 weighings, and you have to identify the 
> fake coin and whether it is lighter or heavier than the genuine coins.
> For each weighing, you have to decide which coins to put on the left 
> scale and which to put on the right scale. You will be told which side is 
> heavier.
> For instance, you may choose to put coins A, B, C on the left scale and 
> D, E, F on the right scale.
> Then if A was the fake and it was lighter, the right scale would go down.
> On the other hand, if the fake was one of G ... L, the scale would stay 
> level. 

Hi ba'c Minh, va ca'c ba'c <>,

bai na`y tui dda~ gia?i lau la('m ro^`i, va` tui cung rat thi'ch no'
Tui pha?i mat 10' mo+'i nho+' la.i mi`nh gia?i nhu+ the^'na`o. -Day la 
solution:

neu	(A B C D) = (E F G H) qua' ddo+n gia?n. fake o+ trong I K L M ....
(Trong truong ho+.p na`y se~ co' truong ho+.p ti`m ra fake coin nhu+ng k0 
biet no' na(.ng ho+n hay nhe. ho+n)

neu	(A B C D) > (E F G H) (1)

ru't 3 coins (D G H) ra khoi ca^n, _chuye^?n_ (B C) sang ca^n ben phai?, 
_chuye^?n_ E sang ca^n ben tra'i, the^m "normal" coin I va`o ca^n be^n 
tra'i. Ta dda~ CHYE^?N CHO^~ 3 coins (B C E).
 
Ta so sa'nh (A E I) va` (B C F): co' 3 kha? na(ng sau:

1) neu 	(A E I) = (B C F) => fake coin is in (D G H) tu+` (1) suy ra lo+i 
gia?i trong 2 truong ho+p co`n lai fake coin se~ na(`m trong 5 coins A F 
&  B C E

2) neu	(A E I) > (B C F) (2) => fake coin is in (A F) vi`: neu no' na(`m 
trong (B C E) (1) se~ "ddo^?i da^'u" tha`nh (A E I) < (B C F) vo^ ly' 
vo+'i (2). Tie^'p theo so sa'nh A vo'i 1 coin tha^.t na`o ddo' dde^? xuy 
ra ket qua?.

3) neu (A E I) < (B C F), ba^'t dda(?ng thu+'c (1) ddo^?i da^'u, vay fake 
coin fa?i na(`m trong 3 coins (B C E) ma` ta dda~ -DO^?I CHO^~ sau la^`n 
so sa'nh thu+' nha^t.

-Dem so sa'nh B va` C, ne^'u = nhau, => fake coin la` E va` nhe. ho+n.
		       ne^'u B > C fake coin la` B va` na(.NG HO+N (suy 
ra tu+` (1).

-Da.i y' nhu+ vay, ba'c na`o co' can dda?m kiem tra ho^. xem to^i co' sai 
cho^~ na`o k0. Thanks.

La^u ro^`i tui cung ho?i ca'c ba'c vo+'i truong ho+.p 13 coins co' 1 fake 
coin, ca^n ba la^`n dde? tim ra. Nhu+ng mai chu+a co' loi giai. Ca'c ba'c 
HU? TOA'N ddau roi.

best,
    ,    ,
   ("\''/").___..--''"`-._
   `o_ o  )   `-.  (     ).`-.__.`)
   (_Y_.)'  ._   )  `._ `. ``-..-'       Me`o tra('ng hay me`o dden
 _..`--'_..-_/  /--'_.' .'               mie^~n thi.t ngon la` ddu+o+.c
(il),-''  (li),'  ((!.-'


                                                Vu~ Quo^'c Hu`ng
						hung@vsb.cz.
+---------------------------+----------------------------------------+
     "Bill Gate's daughter will be the best product from MS".