Numeral systems

today I will write a post about numeral systems and how they generally work. I already wrote about binary and decimal system, but in the last week I did some research on generally numeral systems.

So, just to recap. We normally use decimal system, this means that we use ten symbols to represent numbers, from 0 to 9. First place of number is the number itself, second position represents the number times 10 because we are in decimal system and 3rd represents number times 100 and so on. The general formula to transfer numbers to decimal system goes like this:

anbn + an − 1bn − 1 + an − 2bn − 2 + … + a0b0

a stands for the number that we see written, b stands for the system it is written in, n is the digit where a is –> 0 is the first place.

For example 1334 in the numeral system “7” would be:

4*1+3*7+3*49+1*343=515 in decimal system.

Note how you can represent easily any number in any system because of how the exponents rise in every single digit by one. If the numbers before the next digit are all full, like x9999 in decimal system or x4444 in base 5 system you always need to add only one to reach the next digit, this way there are no numbers left out.

What I really like is that if you had a machine that could change from any numeral system to other you could multiply numbers extremely easily. In decimal system if you multiply by 10 it is very easy because you just add one zero, why? Because all the numbers are “multiplied” by 10 with some exponent already and you just add one which moves all of the numbers to left. In binary system if you multiply by two you just move all the numbers by one digit:

101010111*10=1010101110      (10 is 2 in decimal) Or in 6 base system:
420351234*10=4203512340   (10 is 6 in decimal)

You are basically multiplying by “10” though you need to remember that the number is still in that system.

What about rational numbers? The stuff behind point?

I was really wondering about this and Wikipedia helped out! The exponents are simply negative as in the example below (binary number 10.11 to decimal system):

1×21 + 0×20 + 1×2−1 + 1×2−2 = 2.75

First place –> exponent 0
Second place –> exponent 1
First place behind point –> exponent -1Second place behind point –> exponent -2

Thats it for today.


Eating the spiciest natural chilli

last Sunday I was at neighbors with my host family for dinner. We ate some pumpkin soup and then I noticed these nice small peppers piled up in the bowl. Already I heard that it is not good to put them in your food so I decided to take it as challenge and take one. People at the table noticed and warned me that I probably do not want to eat it. I was soon persuaded not to take it and rather wanted my host brother to try it and see how it goes.

Yup, this is what it looks like.

“These peppers are the spiciest natural growing peppers.”
“Oh, ok then.”

He said that he is going to split with me. I finally agreed and stuffed half of the pepper into my mouth with some milk next to me and bread with thick layer of “Philadelphia”

This is called lifesaver.

After few bites it started to burn a lot. It is quite nasty but the real pain came when I swallowed for the first time. When it hurts in the mouth you can just calm it with bread as it touches the sides of your mouth but when you throat starts to burn it is way more difficult. In something like 15 minutes it was over. Not so much because of pain but simply the pepper, I cried a lot but hey it was quite interesting.

If you decide to try it out, there is one thing to keep in mind. The pepper is going to burn more than one time, actually it might burn three times.. you will know what I mean after you eat it 😉

Anyway there is a chart called Scoville scale, I thought I already wrote about it but then could not find it so here you go.

Spicy peppers have inside neurotransmitter called capsaicin. It fakes your feeling as it bounds on the nerves that are responsible for you to experience heat. Capsaicin is not solluable in water which explains why it wont help you to drink it when you eat something spicy. Milk is better and dairy products generally help. HCl of course helps too.

Capsaicin itself has 16 million points on Scoville scale which is about 8 times as much as the spiciest pepper which is right now Carolina Reaper with individuals well over 2 million. The pepper that I was eating is 1.5 million almost (which is average) and it is called Trinidad Scorpion Butch T Pepper.


Solution to 12 coins balance problem

in the last post I described this cool balance problem with 12 coins where one of them is false one (heavier or lighter than others). You are allowed to weight them 3 times to find out which one of them it is and if it lighter or heavier.

The hint that I gave you is to separate them on 3 groups of 4 coins. Otherwise it is not possible to solve it. For the first one there are two options as you weight 4 coins against 4 coins.

If the outcom is even it goes as follow:

  1. If nothing happens the 4 coins that you have not used must have the false one. Now this is quite tricky. You have probably come out to this part but you have to use all the facts that one weighting will get you as you will see. If something goes down, it is good to know it and vica versa.
    1. a) Now you know that the rest of the coins (4) have to have the false one since it was even. You take one away and put the three against 3 that you are sure about (you have 8 of those). If it is even you know that it is the last coin and you just weight it against one of those normal ones to see if it is lighet or heavier. If you find out that one of the three has to be false you will remember if they were heavier or ligher. Then you take two of them and weight them against each other. The one that did the same thing like in the last weighting is the false one. (If in the 3 vs 3 it was heavier you are searching for the heavier side again.) If they are even you know that it is the last one.
  2. Now it can also happen that one side from the first weighting is heavier than the other. All of the 8 coins are unknown but you can use the fact that one went down and the other up so you need to remember that fact. You also need the 4 coins that you know must be all ok. Put three of those on the “lighter” part. From the lighter part move three original to “heavier” part and from there away three.
    1. b) The easiest thing is when the heavier part is again heavier. Then it has to be one of the original coins from both side which are only 2. You weight one of them against any other coin to get the result.
    2. b) If the part that was heavy is lighter this time, one of the three coins that you moved from lighter to heavier last time must be the wrong one. It is also lighter as you know. Weight two of them against each other. If they balance it is the third one if they do not it is the lighter part.
    3. b) If they balance it must be one of the three coins that we removed completely. We use the procedure described in the last post to find the solution, it is heavy coin then.

Now that is for solution. It is not easy to come up with it and there are some even more difficult versions. Thanks for reading and thanks to Wikipedia for the solution.


12 coins balance problem

today, in this short post I want to show you this cool puzzle that I first encountered on my summer camp. The problem goes like this:

You have got 12 coins. One of them may be false one. You can not know by looking but you have a balance weights. You are allowed to use it 3 times and find out which one of the coins is heavier or lighter (you do not know and it might happen that none is).

I really recommend you to try it out. I almost had a solution though when I checked it I saw that I had mistake in one of the scenarios. Try it out for yourself and in next post I will reveal the solution.




Try to take first step of weighting 4 coins against 4 coins, it will help you 😉



again, it is kind of late so today I will only share with you some cool XKCD pictures and next post will probably be about our asteroid exploration which has 2 major news.

Meteorite Identification

Not the best one but surely up-to-date.


Yeah cameras are great 😉

Pyramid Honey

Thats how conspiracy is created.

To everyone who responds to everything by saying they've 'lost their faith in humanity': Thanks--I'll let humanity know. I'm sure they'll be crushed.


All comics are from XKCD site, thanks Randall

Book review 11) Secret diary of chinese empress

Výsledek obrázku

Czech edition of the book

today in my week plan I finished this book above. It is called the Secret diary of chinese empress though I guess that this book does not even exist in english version.

Book: Secret diary of chinese empress

Author: Johannes Fabricius

Genre: Diary, historical

Pages: 231

Rating: 8.7/10

This book is simply diary of empress Cixi who lived from 1835 to 1908.[1]

Cixi was borned in lower class in China. She was lucky enough to be selected as a concubine for new emperor Xian Feng. Her friend was selected too and soon she was getting lot of attention from emperor.

After a while she was heavy with child and it was clear that emperor will die soon enough since he spent most of his time in brothels and opium dens. He was weak and sick.

After he died she and his wife took the role of regents before her son was 17 years old. That was huge turning point in her reign. She now got most power because her co-regent was not so strong. Of course problems soon appeared. Western fleets and armies took China by attack. With much better technology and tactics they soon overhelmed China that had to agree upon their terms.

There was huge amount of intrique before she was able to get rid of all her enemies which were for example Xian Feng’s brothers.

About 40 years later, again the court had to escape Forbidden City because of what is called Boxer Rebellion, event that was action against various western countries to stop their “expansion” in China. Boxer Rebellion stopped as a fiasco because again, western technology was far better than Chinese.

The painting by Katharine Carl of Cixi.

Cixi died at the age of 72 years and she was called the Old Buddha.

This book was great really. From her diary you do not get much of what is happening in the world. This I think nicely shows that she really did not care and even hated everything that was not traditional. Basically it was her who started the last unnecesarry war that had to lead to her defeat. In the book, though of course she does not say it, she lives very opulently. Rebuilding palaces when Chinese treasury is almost empty. At the same time, she was quite good in what she was doing, like it or not, she reigned for 47 years.

If you can find this book, read it. Quite good to get the idea of how it looked like in China before the WWI.


[1]I guess that the author, Johaness Fabricius only put the book together and made first transletion.

How to! 5) Multiply two digit numbers in your head

today I was sitting outside, chilling out and just as that I started to multiply numbers always adding one: 1*1=1 2*2=4 3*3=9 and so on. And I wondered, how far can this go without paper or calculator?

Well I finished with 100*100 without leaving single number and after a while I started to use this kind of fast and intuitive technique which in this post will be used only to multiply two same numbers smaller than 100.

Lets say you need to multiply 47*47.   (40+7)*(40+7)

Fourty will be called “base number”. The first thing you need to do is to multiply base numbers to get your base. This is simple because 40*40 is the same as 4*4 plus two zeros which means 1600.

Base is quite easy to remember so you do not need to concentrate on that much. Now we need to combine base numbers with, lets call them “pariah numbers”.

In our case pariah number is 7. You multiply it with base number to get 40*7=280 or simply 4*7=28 (+ zero from base number). Because we have two same brackets we need to multiply this twice and add it which is the same as multiplying your result by 2.


Now just add this “double number” to your base which should be quite easy:


Repeat this one few times and then add the product of two pariah numbers to get the result:


Try this few times, and if you are sure in this simple case try any two digit numbers. It is quite nice way to warm up your brain 😉


Stuff happened!

today I returned from the planned vacation in Poland. It was quite pleasant trip with end in family cottage. During that time I read quite some books so I will probably share some of them with you in future posts. Also I will continue with limits and derivatives. Soon there should be photos from Juno so I will share them with you definitely! I should be leaving 21st to Germany for my year there but they have not found my host family yet so I will leave probably 14th September, at least I will have time pack everything go for haircut and such things. Today is Thursday so see you with regular post on Saturday 😉


My experience with Windows 10

since a while back I was kind of interested in programming and computers and on the camp last two weeks there were lot of nerds to computers I decided to share my experience with Windows 10 upgrade.

Do you remember the annoying notifications from your computer about this new operating system? Maybe you have them even now if you have not upgraded yet. My teacher on geography and computers shared with our class this link to some software that disabled these notifications. It was quite good except that I almost missed the time when Windows 10 is for free, the offer ends 28th of this month I think and I got notified just because I was on another computer.

I of course did not want to miss it because right now Windows 10 costs over 100$ which is not something I can afford. Also Microsoft promises free upgrades now and on. This makes sense, all other operating systems have it like that. At least mobile for example, not talking about Linux which is for free completely. I have heard that it would be logical to cut down the price or extend the possibility to upgrade since they want as many people as possible on the newest system. It would be quite nice if there was then just one system not 4 or 5 Windows where some are compatible to something and some are not.

The upgrade itself went pretty smoothly though it took at least 4 hours -_-. Right now I am turning off all the various features the new OS has since I do not want to be part of sharing all my personal data right to office of Microsoft. Not that they could not see everything right now.. but the age is moving on and this is the way it is.. having too many personal things on computer may be dangerous.. the time of clouds has come and it may happen soon that we wont even have proper harddisk but everything will be somewhere else in the world.


PS: even that this is so called “best windows so far” it is not able to have one wallpaper for each monitor -_- 😀

Back from summer camp!

so I returned yesterday from the summer camp where I was last two weeks I mentioned in the last post. I guess that nothing changes about my post schedule so keep tuned, maybe I will post soon something about limits since I am trying to learn those right now.

Summer camp!
Yey! It was quite fun, lot of new people and so on. The theme was from one czech movie about girl in mill and guy who is searching for princess, though the movie is childish it was very well used by the orgs (organizators).

I can not say too much so publicly because some games are used again next year and you can go there only once a life. One of the most memorable things was the day when we woke up at 1:00 AM and hour later we went for a trip long trip. We were actually walking for quite a while. Just walking……. no I am kidding we stopped for breakfast, also we saw sunrise on the tallest mountain in Czech Republic.. then we walked, and again we walked.. we stopped because we needed to change shoes. The we walked and changed socks. And so on. This three times.. then there was storm and we had to stop on 65.5 kilometers with 2700 meters of cumulative elevation gain! It was “hard-core” trip and we did not finish it because of the storm (there was 15 km left). I would post some pictures if I had any, though you can imagine it was beautiful.