Identify the special one among 12 coins [duplicate]

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  • Twelve balls and a scale

    9 answers

We have 12 coins, and only 11 of them have the same mass. It can be assumed that all coins have identical appearances.

We have a lever.

How can we identify the special coin, by taking measurements from the lever for only three times?


Example:

If we have 6 identical coins and one of them is special because it is lighter, we can identify it by taking measurements from the lever for only two times.

  1. Put three on one side on the lever and the remaining on the other side. The special coin is on the lighter side.

  2. Take arbitrarily two coins from the lighter side and place them respectively on two sides of the lever.

Case I: The lever is not balanced

Then, the special coin is on the lighter side.

Case II: The lever is balanced

Then, the special coin is the one on the lighter side (in the first measurement) that was not taken for the second measurement.


However, in the 12-coin case, we do not know if the special coin is heavier or lighter than the others.

No one in my class was able to solve this puzzle, which was given by our maths teacher as a small brain challenge.

Any idea?

Thanks in advance.

how to identify the default mail configurations in sql server

In Sql server, we can setup multiple email configurations out of which only some were set to default.
I have tried using the following query to get the list of accounts

    select *
from msdb.dbo.sysmail_profile p 
join msdb.dbo.sysmail_profileaccount pa on p.profile_id = pa.profile_id 
join msdb.dbo.sysmail_account a on pa.account_id = a.account_id 
join msdb.dbo.sysmail_server s on a.account_id = s.account_id

So is there any way to identify the default mail configuration profiles.

thanks in advace

Identify the special one among 12 coins

We have 12 coins, and only 11 of them have the same mass. It can be assumed that all coins have identical appearances.

We have a lever.

How can we identify the special coin, by taking measurements from the lever for only three times?


Example:

If we have 6 identical coins and one of them is special because it is lighter, we can identify it by taking measurements from the lever for only two times.

  1. Put three on one side on the lever and the remaining on the other side. The special coin is on the lighter side.

  2. Take arbitrarily two coins from the lighter side and place them respectively on two sides of the lever.

Case I: The lever is not balanced

Then, the special coin is on the lighter side.

Case II: The lever is balanced

Then, the special coin is the one on the lighter side (in the first measurement) that was not taken for the second measurement.


However, in the 12-coin case, we do not know if the special coin is heavier or lighter than the others.

No one in my class was able to solve this puzzle, which was given by our maths teacher as a small brain challenge.

Any idea?

Thanks in advance.

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My cousin found this spider at his place. He lives near Milan, Italy, in a small town. It’s a humid region, around there the are a lot of fields but it is a 15 km from the city. It’s still hot in these days. He told me that in the picture it seems a little bit too yellow. In reality it is more of an orange shade. He has never seen anything like that around there. Any clues?

the misterious spider

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Identify clusters with specific properties in binary matrix

My question is somewhat similar to this one, but has some properties specific to it that I think makes it a non-duplicate. I have a binary matrix of nominal categorical values for a set of users:

user group  1   2   3   4   5  ... 10000+
-----------------------------
A    1      1   0   1   0   1
B    1      NA  1   0   1   0
C    1      1   0   1   1   NA
D    2      0   0   0   0   0
E    2      0   1   0   1   0
F    2      1   0   0   1   0

It is known that a user will always be one of two groups; a user will never be in both groups.

The binary data is generally going to be random across users, but in a small portion of the columns (<5%), one group is going to have all 0's. In these particular columns, the data for the other group is still going to be random.

There is a small amount of error in the data, which can cause a 1 to appear as 0, and vice versa (not sure yet if actually relevant or something that I can do anything about). There are also occasional missing data values (depicted by NA above).

The question is, what would be recommended approaches for identifying the columns that would allow me to identify which users belong to each group?

I was leaning towards clustering approaches (no idea which ones), but see other types of approaches mentioned (like in the post I link above).

I have group information for users that would possibly allow me to just programmatically identify these columns, but I would like to try and find an approach for situations where that information is not available, and use the group information I have as a verification tool.

I did try a Multiple Correspondence Analysis (MCA, rather than a PCA given the categorical nature of the data) because it was quick to do, but don’t see anything particularly interesting as far as my goal is concerned.

How to identify recommendations for the target variable using regression? eg: how to maintain target variable…

There are around 48 dependent variables and all are numeric. Target variable is also numeric and it has to be maintained at a particular value. How to relate influencing parameters identified using different regression techniques with maintaining target variable under maximum limit, Any recommendations please?
I’ve so far tried multiple linear regression, stepwise regression, random forest, ridge and lasso regression. Any other techniques would fit this scenario?