12 Balls Puzzle

The Problem:
You have 12 balls identical in size and appearance but 1 is an odd weight (could be either light or heavy). You have a set scales (balance) which will give 3 possible readings: Left = Right, Left > Right or Left < Right (ie Left and Right have equal weight, Left is Heavier, or Left is Lighter). You have only 3 chances to weigh the balls in any combination using the scales. Determine which ball is the odd one and if it's heavier or lighter than the rest. How do you do it?
The Solution:
Number the balls 1, 2, 3, ... 10, 11, 12
Start off with them in 3 groups: [1, 2, 3 and 4], [5, 6, 7 and 8] and [9,10,11 and 12]
Weigh 1, 2, 3 and 4 vs 5, 6, 7 and 8 with 3 possible outcomes:
1. If they balance then 9,10,11,12 have the odd ball, so weigh 6,7,8 vs 9,10,11 with 3 possible outcomes:

1a
If 6,7,8 vs 9,10,11 balances, 12 is the odd ball. Weigh it against any other ball to determine if heavy or light.

1b
If 9,10,11 is heavy then they contain a heavy ball. Weigh 9 vs 10, if balanced then 11 is the odd heavy ball, else the heavier of 9 or 10 is the odd heavy ball.

1b
If 9,10,11 is light then they contain a light ball. Weigh 9 vs 10, if balanced then 11 is the odd light ball, else the lighter of 9 or 10 is the odd light ball.



2. If 5,6,7,8 > 1,2,3,4 then either 5,6,7,8 contains a heavy ball or 1,2,3,4 contains a light ball so weigh 1,2,5 vs 3,6,12 with 3 possible outcomes:

2a
If 1,2,5 vs 3,6,12 balances, then either 4 is the odd light ball or 7 or 8 is the odd heavy ball. Weigh 7 vs 8, if they balance then 4 is the odd light ball, or the heaviest of 7 vs 8 is the odd heavy ball.

2b
If 3,6,12 is heavy then either 6 is the odd heavy ball or 1 or 2 is the odd light ball. Weigh 1 vs 2, if balanced then 6 is the odd heavy ball, or the lighest of 1 vs 2 is the odd light ball.

2c
If 3,6,12 is light then either 3 is light or 5 is heavy. Weigh 3 against any other ball, if balanced then 5 is the odd heavy ball else 3 is the odd light ball.



3. If 1,2,3,4 > 5,6,7,8 then either 1,2,3,4 contains a heavy ball or 5,6,7,8 contains a light ball so weigh 5,6,1 vs 7,2,12 with 3 possible outcomes:

3a
If 5,6,1 vs 7,2,12 balances, then either 8 is the odd light ball or 3 or 4 is the odd heavy ball. Weigh 3 vs 4, if they balance then 8 is the odd light ball, or the heaviest of 3 vs 4 is the odd heavy ball.

3b
If 7,2,12 is heavy then either 2 is the odd heavy ball or 5 or 6 is the odd light ball. Weigh 5 vs 6, if balanced then 2 is the odd heavy ball, or the lighest of 5 vs 6 is the odd light ball.

3c
If 7,2,12 is light then either 7 is light or 1 is heavy. Weigh 7 against any other ball, if balanced then 1 is the odd heavy ball else 7 is the odd light ball.

For command line syntax example

You can use something like this for setting the DNS/WINS server to 10.100.0.1
This scripts will work only locally on the DHCP server.

The “script” fill search all the scopes and then based on their names is setting the optionvalue 5, that is the DNS Server

for /F "tokens=6 delims= " %%A in ('netsh dhcp server dump^find "add scope"') do netsh dhcp server scope %%A set optionvalue 5 IPADDRESS "10.100.0.1"

For the WINS server you can use the optionvalue 44 if I’m remember well :

for /F "tokens=6 delims= " %%A in ('netsh dhcp server dump^find "add scope"') do netsh dhcp server scope %%A set optionvalue 44 IPADDRESS "10.100.0.1"

To use it for a specific DHCP server change it to :

for /F "tokens=6 delims= " %%A in ('netsh dhcp server IP_OF_DHCP_SERVER dump^find "add scope"') do netsh dhcp server IP_OF_DHCP_SERVER scope %%A set optionvalue 5 IPADDRESS "10.100.0.1"