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Xiangyang Liu 刘向阳 - Professional Profile



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GeneralAnswer to IQPOTD Pin
Xiangyang Liu 刘向阳21-Jul-04 0:55
Xiangyang Liu 刘向阳21-Jul-04 0:55 
Here is the answer to the problem[^] I posted a few days ago in the lounge.

We are given 12 balls that look identical and we know only one of them has a different weight. We are also given a scale that can be used to compare weights of any two subsets of the 12 balls. The problem is find a way to determine which ball has a different weight than the rest by using the scale only 3 times.


Let {B01, B02, ..., B12} be the 12 balls. First, compare weights of {B01, B02, B03, B04} and {B05, B06, B07, B08} using the scale.

Case 1

If the two subsets have the same weight, then the odd ball is in {B09, B10, B11, B12}, other 8 balls all have normal weight. Now it is easy to determine which one in {B09, B10, B11, B12} is the odd ball by using the scale only 2 times (this is left as an exercise).

Case 2

The two subsets have different weights, the odd ball is in one of the subsets and all balls in {B09, B10, B11, B12} are normal. We can further assume that {B01, B02, B03, B04} is heavier than {B05, B06, B07, B08}.

Now we use the scale to compare weights of {B01, B02, B05} and {B03, B04, B06}.

Case 2.1

If {B01, B02, B05} and {B03, B04, B06} have the same weight, then the odd ball is either B07 or B08. We can determine which it is by comparing weight of B07 with anyone of the normal balls.

Case 2.2

If {B01, B02, B05} is heavier than {B03, B04, B06}, then the odd ball is in {B01, B02, B06}. This is because we already know {B01, B02, B03, B04} is heavier group from the previous use of the scale. Now we can determine which one is the odd ball by comparing B01 and B02, if they have the same weight, then B06 is the odd ball, otherwise the heavier one is.

Case 2.3

If {B01, B02, B05} is lighter than {B03, B04, B06}, then the odd ball is in {B03, B04, B05}. We determine which one is the odd ball by comparing B03 and B04, if they have the same weight, then B05 is the odd ball, otherwise the heavier one is.







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GeneralRe: Answer to IQPOTD Pin
netclectic22-Jul-04 5:37
netclectic22-Jul-04 5:37 
GeneralRe: Answer to IQPOTD Pin
Xiangyang Liu 刘向阳22-Jul-04 6:17
Xiangyang Liu 刘向阳22-Jul-04 6:17 
GeneralXYMailClient vs MSMAPI32.OCX Pin
adrig23-Feb-05 10:23
adrig23-Feb-05 10:23 
GeneralProblem with ODBCService Namespace Pin
jontulley20-May-05 4:26
jontulley20-May-05 4:26 
GeneralRe: Problem with ODBCService Namespace Pin
Xiangyang Liu 刘向阳20-May-05 6:58
Xiangyang Liu 刘向阳20-May-05 6:58 
GeneralRe: New Topic Pin
rahul_spi26-May-05 2:36
rahul_spi26-May-05 2:36 
GeneralRe: XySystem message processing speed Pin
tophat00026-May-05 19:36
tophat00026-May-05 19:36 
GeneralRe: XySystem message processing speed Pin
Xiangyang Liu 刘向阳27-May-05 0:40
Xiangyang Liu 刘向阳27-May-05 0:40 
GeneralRe: XySystem message processing speed Pin
tophat00027-May-05 11:23
tophat00027-May-05 11:23 
GeneralRe: XySystem message processing speed Pin
Xiangyang Liu 刘向阳27-May-05 13:18
Xiangyang Liu 刘向阳27-May-05 13:18 
GeneralYour articale about sending a window message to a program running on remote host Pin
DavidR_r18-Jun-04 2:44
DavidR_r18-Jun-04 2:44 
GeneralRe: Your articale about sending a window message to a program running on remote host Pin
Xiangyang Liu 刘向阳18-Jun-04 4:03
Xiangyang Liu 刘向阳18-Jun-04 4:03 
GeneralHow to install XYNTService under an account besides Local System Pin
john.berry23-Jun-04 7:03
john.berry23-Jun-04 7:03 
GeneralRe: How to install XYNTService under an account besides Local System Pin
Xiangyang Liu 刘向阳23-Jun-04 7:48
Xiangyang Liu 刘向阳23-Jun-04 7:48 
GeneralRe: How to install XYNTService under an account besides Local System Pin
john.berry23-Jun-04 8:07
john.berry23-Jun-04 8:07 
GeneralInvokeMethod & PropertyGet vs. DispatchMethod Pin
brafalowski13-Jul-04 16:29
brafalowski13-Jul-04 16:29 
GeneralRe: InvokeMethod & PropertyGet vs. DispatchMethod Pin
Xiangyang Liu 刘向阳13-Jul-04 22:37
Xiangyang Liu 刘向阳13-Jul-04 22:37 
GeneralInvoke Failure Pin
brafalowski16-Jul-04 15:49
brafalowski16-Jul-04 15:49 
GeneralRe: Invoke Failure Pin
brafalowski17-Jul-04 7:15
brafalowski17-Jul-04 7:15 
GeneralASP running as a service! Pin
n30n19-Jul-04 7:10
n30n19-Jul-04 7:10 
GeneralRe: ASP running as a service! Pin
Xiangyang Liu 刘向阳19-Jul-04 7:12
Xiangyang Liu 刘向阳19-Jul-04 7:12 
GeneralRe: New Topic Pin
dalaroseyeah30-Apr-04 1:42
dalaroseyeah30-Apr-04 1:42 
GeneralRe: New Topic Pin
Xiangyang Liu 刘向阳30-Apr-04 1:51
Xiangyang Liu 刘向阳30-Apr-04 1:51 
GeneralXYDispDriver Return Types Pin
brafalowski26-Apr-04 2:15
brafalowski26-Apr-04 2:15 

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