Identify the special one among 12 coins [duplicate]

This question already has an answer here:

  • 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.

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.

What is the term for special words that don’t use standard readings or regular modifications? [duplicate]

This question already has an answer here:

  • How to classify the non-standard reading of “お土産{みやげ}”?

    2 answers
  • Where does the な in 大人 (otona) come from?

    2 answers

Words like 大人、下手、上手… as おとな, へた, じょうず.
What is the name for terms of this type?

Not including:
Kanji that don’t use their specified readings.
The answers for おみやげ don’t answer the classification of non-standard pronunciation (they answer other questions but the stated one).
The おとな related question is very specific to that word.
I believe the other stated duplicate doesn’t answer this in general either.
It would very hard for a searcher to find these somewhat duplicate questions.

Is there a list of Windows special directories/shortcuts (like %TEMP%)?

I’m looking for a reference list of shortcuts like %TEMP%.

When I’m using Windows+R or Windows Explorer and type %temp%, the Windows Explorer takes me to the Temp directory. Are there more of these shortcuts?

UPDATE:
I found a helpful reference page for environment variables (might not be up-to-date with Windows 7).

How to display Catalog Price Rule Discount and Special Price Discount along with Cart Price Rule Discount?

I’m using Magento version 2.2.4.
Currently on view and edit checkout page, only Cart price rule discount is shown as below

enter image description here

How to show Catalog Price Rule and Special Price (added while adding a product in Admin panel) in same or another line on checkout index page?

Special order filter (by language) in CP for Craft Commerce

We have a online-shop for german customers (Craft 2 + Commerce 1) and will expand the shop for american customers (via second domain).
Is there a way to filter the order (status) views in the Backend by domain/language.
The purpose is that the american backend user should only see orders that come via the american domain and the german backend user should see only german based orders.

Was there a special drive, that saved much more than 1.44MB on an HD floppy disk?

I think that I have once seen an Internet article, which stated, that special drives are capable of making many megabytes of data out of one ordinary MF-2HD floppy disk. But I am unable to find it again.

Did such a drive actually exist?

Is there any more accurate documentation about this technology? Is there any way to store 32MB on a MF-2HD in 2018? And what aboue DD and ED disks?


I found more information here:**

  • http://www.theregister.co.uk/2000/10/23/32mb_on_a_humble_floppy/ 32MB on a humble floppy
  • http://en.wikipedia.org/wiki/Floppy_disk (that’s where I probably read it one day: “For example, the LS-240 drive supports a 32 MB capacity on standard 3½-inch HD disks,[54] but it is, however, a write-once technique, and requires its own drive.”)

Wikipedia article mentions Zone Bit Recording.

Because the sectors have constant angular size, the 512 bytes in each
sector are compressed more near the disk’s center. A more
space-efficient technique would be to increase the number of sectors
per track toward the outer edge of the disk, from 18 to 30 for
instance, thereby keeping nearly constant the amount of physical disk
space used for storing each sector; an example is zone bit recording.

Is that high density writing technology with 32MB still CAV or CLV like optical discs (CD, DVD, HD-DVD, BD, etc.)? Does it utilize ZBR?


Answer on other question by @ChenMunka:

http://retrocomputing.stackexchange.com/a/5449/7641

You would not expect a quick format to repair corruption from magnetic fields as it doesn’t recreate the track and sector sync markers.

This means, that the track sector information can be written on a format. Does that not mean, that an ordinary drive could possibly squish like 10MB on a floppy disk by formatting it with different track/sector information?

to format or write to this high-coercivity media, the high-density drive switched its heads into a mode using a stronger magnetic field. When these stronger fields were written onto a double-density disk (having lower coercivity media), the strongly magnetized oxide particles would begin to affect the magnetic charge of adjacent particles. The net effect is that the disk would begin to erase itself.

How long does it take for the floppy disk to erase itself when treated like an ED? Can I store 2.88MB on MF-2HD for 10 minutes?

clustering evaluation for a special case

In my dataset each point comes from one of 3 classes, so the true labels are like [0,1,0,0,0,2,1....]. I have to cluster them in 200 clusters. I want each cluster to contain more points from the same class. So,
a cluster such as [0,0,0,1] (C1) is a good cluster, whereas [1,2,1,0] (C2) is not.

I am trying to come up with an evaluation strategy for this. The harmonic mean of class frequencies seems like a starting point. For C1, it would be (1/3)+(1/1)+(1/(0+eps)), for C2: (1/2)+(1/1)+(1/1). Taking eps=0.1, obviously, C1 has a higher score.

But this would be affected by cluster size. Is there a way to eliminate that? Or better, does any evaluation protocol exist in the literature for this problem?

EDIT

I am trying to create a codebook of visual words from images. I have N images from 3 classes. These 3 classes are the true labels.

From each image, F number of d dimensional feature descriptors are created. So I have a data matrix of N*F rows and d columns. These are clustered in 200 clusters and the cluster centers are combined to create the codebook. I believe This is a standard procedure for this problem (https://en.wikipedia.org/wiki/Bag-of-words_model_in_computer_vision).

I expect the clusters to have some kind of homogeneity, i.e., in each cluster, most data points should from one class of image.

Is there an in-universe explanation in the 90s Iron Man cartoon as to why he can summon his special suits?

Tony Stark can summon his suits (and in the fighting video games where he appears, his weapons) that aren’t nearby (i.e. you don’t see him telling JARVIS to have them on standby or to follow him).

Is any in-universe explanation for this?