Miscellaneous Problems In Maths

Every answer needs to have steps. 

1. There is a cubic box of size 1m by 1m by 1m. It is filled to its capacity with solid spherical marbles, all of the same size. Then the box is filled with water. What should be the radius of the marble so that max water can be filled. And what is the minimum volume of water than can be filled? 
2. There is a circular park which has a path on the outside. What should be the ratio of the inner radius of the park to the width of the path so that the area of the path and that of the park are the same?

Additional reading

1. http://vbala99.blogspot.com/2015/06/maths-and-logic-puzzles.html
2. 
   

Working On Filtered Data

Problem no: 1

Let's assume there is a table in Excel with 10 rows and having data in columns A to J.

How do we find sum of all  the cells in all the rows and columns mentioned above. There are filter conditions to be applied on some rows as well as on some columns. 

Assume we have frozen the panes in the excel so that row headings are frozen to the left (say cols A and B) and column headings (say row 1) on top. Now filter conditions have to be applied on cols A and B and row 1. 

Countifs and Sumifs won't work on both rows and columns. How will you address this?

Problem no: 2

Now let's assume we need to find the minimum (or max or average) value in a column while also applying a filter on another (or same) column. How do we do that?

Additional reading:
A friend sent me this nice article on Vlookup: https://exceljet.net/things-you-should-know-about-vlookup

Recipe - Chakkarai Pongal, Badam Halwa, Gaajar Ka Halwa

Chakkarai Pongal:

Boil moong dal and rice in the ratio 1:4. Mash the boiled mixture. Boil water and then mix jaggery. Jaggery by volume should be twice (actually about 1.75 times) the volume of rice + moong dal used to boil. Water should be just enough to cover all the jaggery. Filter the jaggery solution and throw away any solids (typically dirt). 

Add ghee and stir the water - jaggery + ghee mixture until it starts foaming. Add elaichi powder. Transfer the jaggery + water to the mashed rice + dal and mix well. சக்கரை பொங்கல் ready.

Water being boiled

Jaggery to be added. It was mashed in the dark container. Moong dal and rice mixture to be boiled (after adding water)

After adding jaggery to water

Stir. Filter out extra water.

After adding rice-dal and ghee. Almost over. Made on Pongal day 2017.

Almond (Badaam) Halwa

Heat almonds in boiling water. Cover the vessel and let it soak for couple of hours then peel the skin. (Maybe we could pressure cook almond). Then grind almond and get a paste. Make cheeni paagu by heating sugar in water. Mix the paagu and almond paste and heat. Keep stirring while adding ghee. Add saffron towards the end. This is very similar to chakkarai pongal except for jaggery, use of almonds and how almond is processed. 

Carrot (Gaajar) Halwa:

Grate 3 carrots. Boil half liter of  full cream milk. Keep stirring. Add grated carrot when the milk volume has shrunk. Finally add about 175 ml of sugar and keep stirring. That's all.

Boil milk in a large container and keep stirring

Grate Carrot

Add Grated Carrot to Boiling milk when milk has shrunk

See how thick  it becomes

About 175ml sugar to be added, right at the end

Almost the final stages

Finally, Gajar Halwa. (Unfortunately, red color shows up as yellow in my phone's camera.)

Additional Reading:

• http://vbala99.blogspot.com/2016/08/making-sambar-and-rasam-powder-and.html
• http://vbala99.blogspot.com/2015/08/a-list-of-indian-mostly-tamil-lunch-and.html

Recipe: Making Ghee From Home Made Butter

Making Ghee From Home Made Butter:

This consists of a few distinct steps (this is for buffalo milk - I don't think it's much different for cow milk). The steps (bullet points) are in reverse order.

1. Heating the butter in a kadai for about 20 minutes with constant stirring until you get ghee: I take the butter out from the freezer. It will be frozen. Wash it in tap water (hopefully it removes  any remnants of buttermilk). Then transfer the butter to a kadai and heat it. The butter color will change from white to yellow to green to brown and then froth.. Then you switch off the gas and let the ghee cool down (filter out the kashandu - dark brown or black solid stuff and, well, eat it) and store the liquid ghee in the fridge. I get about 1 liter ghee per 45 liters of buffalo milk. The milk is from a milkman (not Aavin). This works out to about 2% ghee to milk ratio. I have friends who get almost double of what I get.. That (getting 3%), I think is true expertise.
2. Taking butter out from aadai (or malaai): I make butter every alternate day. I take the aadai out from the fridge, pour it into a tall vessel and add a glass of water and let it almost come to room temperature. Then I use a hand mixie on the tall vessel containing the aadai for about 7 to 8 minutes. Then I switch off electricity and slowly move the hand mixie in a circular fashion for about a minute so that the butter coagulates. Switch electricity on for 2 to 3 more minutes and then off and rotate the hand mixie again. Now butter should have formed. I use my palm to scoop off the butter and store it in a box. I would then add another glass of water and repeat the hand mixie stirring process once again and get a little more butter out, which I again transfer to the box. You can drink the remaining butter milk. I put the box containing the butter in the freezer. I collect butter 3 times over a period of 7 days (once every 2 days) before making ghee.
3. Taking cream (aadai) from milk and yoghurt: Boil the milk. Use it for coffee etc, if you have to, making sure that you don't pour out aadai along with the milk. Boil it once again. Let the milk cool down and then store the milk in the fridge. Take it out from the fridge, take out the aadai and store the aadai in a separate container. When you make curd from the milk, transfer the top layer of the curd using a spoon into the aadai container. Essentially, the aadai comes from both milk and from curd. I collect aadai for 2 days before going to the next step of getting butter. The fresh aadai taken from the milk has to spend a few hours outside at room temperature before being moved to the fridge.

Here are photos for step 2, the most critical step:

Aadai transferred to tall vessel and ready to make butter with hand mixie

Stirring with Hand Mixie

You can see butter

Butter to be taken out

Transferring butter

Bottom left is buttermilk: the rectangular box has butter, Conical vessel with a white spoonin the center has ghee, the vessel to the right of ghee with a spatula has curd, to the north of curd is milk. - They aren't in any particular order.

Aadai collected from milk and curd:

Aadai Collected from milk and curd - 

Making Ghee from butter: 

Yellow a few minutes after I start heating

Getting Green

Towards the end: Brown

At the end: ghee almost made

After it's all over:Kashandu at the bottom. With the filter and wooden spatula.

Making cooking ghee:
Buy cooking butter (unsalted) and heat it and stir it to make ghee. Store  it  in a vessel.

Additional Reading:

• http://vbala99.blogspot.com/2016/08/making-sambar-and-rasam-powder-and.html
• http://vbala99.blogspot.com/2015/08/a-list-of-indian-mostly-tamil-lunch-and.html

Repetitive Patterns In Excel

Using Excel (No macros) how would we create a repetitive pattern? For example, let's assume we have the list of students in a school, with their  class, section and we need to print students' labels with the same fields and "Subject" and Year with blanks (to be  filled by students).

A sample label is shown below.

Name: <__________________>

Class: <__________> Section: <________>

Year: <___________> Subject: ________

XYZ School: <_____________>


Now assume we have an excel sheet which contains the student names, their classes and sections as a table (name of school is  also available). How do we use the data in the table to create these labels for all the students using formula?

Next Problem
Create a transpose of an excel table with, say, 5 rows and 6 columns.. Use only formulas.. Meaning in the transpose all formula should be the same (I should be able to copy and paste one cell to all other cells (6 rows and 5 columns) and create the transpose)

Rommel And Canaris (and Guderian) - Rose Among The Nazis (WW II)

World War 2:

Roses:

1. Canaris
2. Erwin Rommel
3. Heinz Wilheim Guderian: 

The Dirty ones:

1. Adolf  Eichmann
2. Joseph Goebbels
3. Reinhard Heydrich
4. Heinrich Himmler
5. SS Women

Additional reading:

1. http://auschwitz.dk/
2. http://ww2gravestone.com/
3. https://en.wikipedia.org/wiki/George_S._Patton%27s_speech_to_the_Third_Army
4. http://vbala99.blogspot.com/2015/05/eichmann-simon-wiesenthal.html

Control Freak

A friend asked me whether a high energy J can't be a control freak. I asked her to find the difference between Naveen Babu - the character played by Saif Ali Khan's father in the movie Parineeta and Anniyan (the negative role played by Vikram in the movie Anniyan). Anniyan was a high energy J (as in MBTI) who was very fussy about discipline and about right and wrong. Naveen Babu, on the other hand, was not about rules. He wanted his wife and his son to do exactly what he said. And he, unlike Anniyan, didn't have a constant set of rules.

Quote from the wiki that describes Saif's father: "Sabyasachi Chakrabarty as Naveen Roy. Cold at heart, a shrewd and a conniving businessman who even places human values and relationships below his greed for money. Surinder Kaur as Rajeshwari. The mother of Shekhar [Saif] who scornfully watches how badly her husband treats the neighbours and gets ill."

Are Naveen and Anniyan similar? Are they both control freaks? Can a J be a control freak? I say No to all questions.

Is every P a control  freak? If the P has low energy then No. Is every high energy P a control freak? No, all P's are not control freaks. I would probably guess that an Enneagram 8 has a high potential to be a control freak. And a control freak is very likely to be a P. 

Why Do Women Always Want To Look Younger

I have always wondered why women tend to reduce their age. And I thought the reason was that they wanted to portray plenty of child bearing years remaining. 

And maybe I was right. Closely related is the topic of biological clock which is very critical and treated as such by women. But men, as far as I have seen, rarely think of themselves as having a biological clock.

Ask any 40 year old woman her age, she is likely to round it off to 37. Now we know why. I  am guessing that if you ask any 9 year old girl what her age is, she won't round it off to 5 - she may want to be considered to be 10 or even 11. She would want to get into the child bearing range without even knowing what it means. Hardwired?

Why Do Human Mothers Feel So Much Pain During Child Birth

This is another post on the Man and Animal series. I had earlier written about rape in man and animals and the cause of difference between man and animals.

The current one is about the excruciating pain that human mothers feel during child birth. The question is: do all mothers feel roughly the same pain or do human being feel and / or express a lot more.

Here are some nice articles on the subject:

1. http://www.slate.com/articles/health_and_science/explainer/2012/09/animals_giving_birth_dolphins_bear_newborns_easily_but_hyenas_risk_death_.html: The ratio of the size of the new born (say 3kg baby in humans) in relation to the size of the mother (say 60kg) can be compared across species. The higher the ratio the more difficult the child birth can be. Nice analysis isn't it?
2. https://www.quora.com/Why-is-the-human-birth-seemingly-more-painful-than-other-mammals: This one again is lovely. Bipeds have a narrower hip and human heads are larger than heads in other species with the result that getting the human baby out is much more arduous.
3. http://community.babycenter.com/post/a24011163/are_we_the_only_animals_with_painful_births: This brings out the point that expression of pain in other species is likely to result in danger from predators to the mother and new borns and hence the mother does not express the pain. Extrapolate (from my earlier article that surmised that human beings think and emote much more than other species) and we can possibly explain why human being cry out a lot more. A quote from the link: "Animals have limited ways to express their feelings and my guess is that birth is painful for many animals, just like it is for many women. There are some women who have experienced pain free and even orgasmic births, but they are a rarity. The majority of women do experience pain and I think likely so do most animals, they just don't have the ability to express it the way we do."
4. http://psychologyofwellbeing.com/201005/why-is-childbirth-so-freakin-painful.html:  I have included this article because it discusses the issue while providing no answer to the question (had this article been submitted in response to my question, I would have rated it "F"). 

Additional reading:

• Inbreeding: https://davidcavill.wordpress.com/a-beginners-guide-to-inbreeding-and-line-breeding/
• Pain in animals (a nice instructive video): https://video.scroll.in/827043/watch-this-is-how-animals-experience-pain-which-they-cannot-always-convey
• http://vbala99.blogspot.com/2016/08/difference-between-man-and-other-animals.html

Rape: Why Are Humans Perpetrating It While Animals Apparently Don't

As I was walking I suddenly had this thought. Why is it that the institution of rape exists only in human beings and rarely / never in animals? If Man evolved from animals then Man has gotten this unique habit recently. Why does he do it - more importantly why did he start raping only after having become Man? 

As I was discussing with a friend while walking.. We came up few ideas in relation to the question raised above.

1. Animals strictly adhere to the "(Female's) No means NO" rule
2. Perhaps females in the human species have a higher expectation from the males than do females in other lower species with the result that more human males are prevented from mating resulting in "need" for giving an outlet to sexual urge
3. Animal kingdoms have a (alpha) male mating with multiple females and hence fewer unattached females are available for copulation and rape by males. Among humans, all males are treated as equals and no one man can have more than one woman at a time. Note that rape can be eliminated by removing all females from the scene.
4. A strict punishment enforced for transgressing males in animals

My friend and I thought that one or more of the points above could have caused human beings to coerce a woman into sex.

At this point in time I am still very confused. My initial belief that rape was a truly human invention is itself wrong. Of course many of the articles say that the term "rape" is inappropriate when used in the context of animals and that the right term is forced copulation. Whatever... A rape by any other name... is still rape.

Additional reading:

1. http://www.livemint.com/Opinion/jkywrmQMip9SG6QVYDoe0H/Rape-in-the-animal-kingdom.html
2. https://en.wikipedia.org/wiki/Sociobiological_theories_of_rape
3. I was fairly sure that gang rape was unique to humans until I read this article (read under bottlenose dolphins and also in the para on ducks): http://english.mathrubhumi.com/news/columns/faunaforum/rape-happens-in-animal-kingdom-too-maneka-sanjay-gandhi-animals-1.1435307
4. Why rape is supposedly high in Sweden - lovely article: https://en.wikipedia.org/wiki/Rape_in_Sweden
5. Nice series of answers to  a similar question: https://www.quora.com/Is-there-really-any-such-thing-as-rape-All-animals-mate-without-incident-of-rape-except-human-beings-What-makes-rape-real-with-men-but-not-apes
6. Another nice article showing how apes do "rape" but is not as bad as human rapes: http://www.npr.org/sections/13.7/2013/10/03/228809153/why-gorillas-arent-sexist-and-orangutans-dont-rape
7. Rapes by animals: http://www.washingtoncitypaper.com/columns/straight-dope/article/13045860/can-dolphins-rape-humans-when-animals-attack-sexually
8. http://www.goodreads.com/book/show/2896628-when-fathers-rape: This book seems to be interesting, unfortunately there is no online version available as of Nov 5, 2016.