Nonogram / Picross Tricks

I occasionally play Nonograms or Picrosses depending on however you like to call them. They're as enjoyable as Sudoku if not more. After a while, you may or may not figure out some tricks to help you solve the puzzles faster. Today I'm gonna share my tricks with you.

Reminder: What Is Picross / Nonogram?

Nonogram also is known as Picross is a number puzzle that gives you mostly an empty grid with numbers on top and on the very left. These numbers work as hints. The number that's to the very left of the row gives you the number of fields that should be marked in this line. The numbers depend on the size of the puzzle. Usually, the puzzles have sizes of five to 15. As such the hint numbers are also from zero to 15, where zero means no fields should be marked. Additionally, the numbers only mark adjacent fields and if multiple ones mean they're spaced, as in they have one or more blocks in between. The numbers on the top do the same as the ones on the left but only for the column. When all the fields that should be marked are so, you will end up with a picture that could be called pixel art. The order also matters. This means if you have a (5, 3, 4) you will have maybe some space then five adjacent fields to mark and then an unknown amount of space three more fields to mark the more unknown amount of space and lastly four fields to mark that may or may not be followed by more space. 

Unfortunately, with the increasing size, the difficulty increases as well. So here are some tricks and why they work that will help you solve the harder ones.

Look For The Full Size

Edited Screenshot from
 http://liouh.com/picross/

Quite a basic one, still one to mention though. If you find a row or column that mentions a number that is equal to the height or width of the Nonogram you can fill out the full row or column.

Sum Equals Full Size

Edited Screenshot from
http://liouh.com/picross/

Similar to the previous one except now we're summing up all of the fields that need to be marked including spaces. In the screenshot we got 2 + 1 + 3 + 1 = 7. There are four groups of fields with each at least one space. Since ten is the maximum per line the spaces need to be exactly the size of one. So we have 2 + 1 + 1 + 1 + 3 + 1 + 1 = 10 with spaces being marked gray and fields blue. If the sum equals the maximum size of the picross (in this case the width, for columns the height) then we can mark them just as they're listed there since the spaces in between can't be bigger than one.

Minimax Overlap

Edited Screenshot from
http://liouh.com/picross/

This is one of the tricks that I use most often. When you have a number that is big enough it creates an overlap that guarantees a field to be marked. Assuming we have a 10x10 picross with an eight. It could either lie from the top left to the right or it could be at the very right to the left. What we notice is that in both cases some fields will be marked either way. This leaves us with a guaranteed 6 fields. Fun fact: Regardless of the size of the picross if the number is greater than half of the height or width than this method starts to work for single numbers. It also works with groups as seen in the example below.

Edited Screenshot from 

http://liouh.com/picross/

Default Overlap and Shifting

Collage of screenshots made from
http://liouh.com/picross/

For single numbers, the minimax overlap will swiftly turn into an automated thing. For example, if you have a 10x10 and you have a single number like six you know there are two fields in the middle that should be marked. Same for a 15x15 having 8 as a single number. You will start to instantly mark the middle field. Additionally, for every increment of that number, you can fill it by two more as seen in the example to the left.

Last but not least the shifting. The default overlap can be shifted easily. For this, we look at the numbers before or after. If the number is before it's a shift to the right if it's after a shift to the left. If it's on top it's a shift down if it's below it's a shift up. We need to count empty fields as well here. The example below shows it. The example is not the best though. If we have something like (1, 8, 2) it would work as we can assume at least one space between (1, 8) and (8, 2). No problem with that. However, if we have another number before or after such as (1, 1, 8, 1) it could be dangerous as we don't know how many spaces are between (1, 1).  So for (x, y, z), shifting works perfectly. For (..., x, y, z, ...) I haven't had enough experience and/or didn't look too deep into it.

Edited Screenshot from
http://liouh.com/picross/

Try It Out :P

You can go and try it out under the gaming section of my blog (though I think I haven't updated those in quite some time... yikes.) or on other websites (there are tons). There are also free mobile apps. That's it from me for now. Happy brain work out!

Guild Wars 2: Tyria's Gravity

Finally, Tyria's gravity has been calculated. Now we can compare to other planets' gravities and maybe draw some new conclusions from it? Anyways we left off by figuring out that Guild Wars 2 does indeed seem to have gravitation.

Next Steps

So, if we assume Guild Wars 2 does indeed have gravity - where things seem to point to - then we can calculate it. Calculating gravity is the same as acceleration. Acceleration is often related to F = m * a. Unfortunately, we know neither F nor m. There's another formula as well though. Acceleration is the change of velocity over time. So, basically a = ∆v / ∆t. Next up is another problem. We don't know the velocity of our character. It's not shown in any kind of way in Guild Wars 2. This means we need to calculate it as well. For this, we have a formula as well. The time it took to get from a position to another or the distance passed in a time frame. That's v = ∆x / ∆t.

The Experiment

Okay, so what we need to do is calculate the velocity at two different points of time that are still related to each other (e.g. different points of time in one fall). To get the velocity we need to calculate how long we take to fall a certain distance. We obviously need some way to tell the time, a watch could do this, however, the fall speed is too great to use a stopwatch this rapidly. Thusly I'm gonna record the fall on video and use the footage and frames to measure the fall speed. As a distance, I'm gonna use the Necromancer's staff traps that provide a 240 unit radius or 480 unit diameter. As a drop, I'm gonna use the one at the Kormir High Road.

To do the experiment I need to start the recording drop down while placing my marks on the wall and then get up as fast as possible, position the camera and jump down. It only took me one try even though it sounds quite stressful.

Analysis of the Footage

Next up, we're gonna analyze the footage. Specifically, we want to mark the two frames that meet the respective points well enough. Then we take the time between those.

As a reminder to calculate the gravitation we use the formula a = ∆v / ∆t with ∆v = v₂ - v₁ with v = ∆x / ∆t with ∆x = pos₂ - pos₁ and ∆t = t₂ - t₁

If we combine everything to a big formula we get: 
a = ((pos_2v2 - pos_1v2) / (t_2v2- t_1v2)) - ((pos_2v1 - pos_1v1) / (t_2v1 - t_1v1)).

Screenshot pos₁ of v₁

The first mark or first velocity v₁ we reach pos₁ after about 30 seconds of the fall. When using Vegas Pro 15 - which was available last year during a Humble Bundle :P - the time is given in hours, minutes, seconds and 1/30th of a second using the format HH:MM:SS:ss. We convert the next smaller unit to seconds by dividing it through 30 and multiplying the result with 100. E.g. 30 / 30s = 1s or 9 / 30 = 0.30s. This point in time in the video is t1 is 29:24, so 29s + 24 / 30s = 29.80s. The second position pos₂ is reached at 30:08 which is 30s + 8 / 30s = 30.27s. This means that ∆t = t₂ - t₁ so 30.27s - 29.8s = 0.47s. We already know the distance as it is the diameter of the staff mark which is

Screenshot pos₂ of v₁

480 units. Now we can calculate the velocity via v₁ = ∆x / ∆t. So our first velocity v₁ is 480u / 0.47s = 1021.28u/s. 

Screenshot pos₁ of v₂

Now on to the second one. We reach this point t₁ in the video at 31:01. That's 31s + 1 / 30s = 31.03s. The second point t₂ at the end of the mark is reached at 31:13 equivalent to 31s + 13 / 30s = 31.43s. Calculating the delta for v₂ we get ∆t = 31.43s - 31.03s = 0.39s.

With this we can calculate the velocity v₂ which is 480u / 0.39s = 1230.77u/s.

Screenshot pos₂ of v₂

At this point I must mention the difference between the first delta time and the second delta time is ∆t = 0.47s - 0.39s = 0.08s. Since my Guild Wars 2 runs at ~30 frames per second and my recording at 60 frames per second we are still limited to the ~30 frames per second from Guild Wars 2. One frame thus, as represented by Vegas Pro is 1/30th of a second. This means that one frame is equal to 1 / 30s = 0.1s. This means the difference between the two delta's could just as well be a measurement error and thus would require more research.

For the rest of the post, I'm gonna assume this is not a measurement error as such I'm gonna continue.

The Finale

Now that we have the two velocities and we can calculate the acceleration. As a reminder, we're gonna calculate the acceleration using a = (v₂ - v₁) / (t₂ - t₁). For t₂ and t₁ we're gonna use the start points pos₁. Filling out the variables we get a = (1230.77u/s - 1021.28u/s) / (31.03s - 29.80s) = 209.49u/s / 1.23s = 170.32u/s². Now to convert this to something that's more familiar to us and less useful for theorycrafting (heh :D) using the conversion from units to metric and to feet:

in metric: 170.32u/s² * 2.52cm/u = 429.21cm/s² | 429.21cm/s² / 100 = 4.29m/s²

in feet: 170.32u/s² * 0.083ft/u = 14.14ft/s²

in mph: 14.14ft/s² / 5280ft/mile * 3600 = 8.64mph

I have a small little book with formulas and data in it that helps students in exams. Let's look at which planet would equal this gravitation. 

Earth with a g-factor of 9.81 is well known. the nearest ones below are Merkur with 3.7 and Mars with 3.71.

Thus we've got us a planet with a little higher gravitational constant than Merkur or Mars.

Now if someone can do the drop with 60 frames per second it would be appreciated. Until disproven... I rest my case. Have a good day/night. 

Fortune Telling: The Principle of Card Reading [2/3]

Okay, so, we clarified that there are some issues with fortune-telling, still, it would be nice to do it nonetheless. You can still avert one or the other disaster or maybe it's nice to know it to tell the difference between fake and real much better or to understand how it works out of curiosity. Whatever the reason may be, let's get into it.

Requirements

To be able to do card reading you need to do some preparation. You need to take care of two things. First of all, you need cards. Card reading isn't card reading without cards, duh. :P Second of all you need a system on where to place the cards. Let's go into the cards first.

Famous Cards

The most famous cards used for card reading are tarot cards. This deck features 22 cards. Each of these cards features a completely different theme. The themes are^[1][2]:

I.	The Magician		XII.	The Hanged Man
II.	The High Priestress		XIII.	Death
III.	The Empress		XIV.	Temperance
IV.	The Emperor		XV.	The Devil
V.	The Hierophant		XVI.	The Tower
VI.	The Lovers		XVII.	The Star
VII.	The Chariot		XVIII.	The Moon
VIII.	Strength		XIX.	The Sun
IX.	The Hermit		XX.	Judgement
X.	Wheel of Fortune		XXI.	The World
XI.	Justice

Each card has its own meaning that is taken from what is represented in the picture. To be able to do card reading you need to familiarize yourself with the meanings of each card. Keep in mind that - as always - your own interpretation also plays a certain role in their meaning. It is very important to realize that you don't need to know the cards in and out but you do need your unconsciousness to know them.

The System^[3]

The system in card reading is the way you place the cards. Here each position where a card will be placed has a meaning. Multiple ways can be found all over the internet. The Celtic cross, for example, has a layout where you lay the cards like this:

The positions share the following themes:

1.	Present		Perception, state of mind of the current happening and the happening
2.	Challenge		An immediate challenge, issue or problem that makes life harder
3.	Past		What lead to the present and maybe the challenge as well
4.	Future		What will happen in the next weeks or months; the next step on the journey
5.	Above		The goal, aspiration or the best outcome of the current situation
6.	Below		Underlying feelings, motivation, drive associated with the situation
7.	Advice		Takes everything into  consideration and gives advice for the challenge
8.	External influences		Represents people, energies or events that have influence on the challenge (things where there's no control over)
9.	Hopes and/or  fears		What is hoped for and/or what is feared
10.	Outcome		Represents the current direction the challenge or situation is taking

The Reading

Now that you are familiar with one way for the system and one deck of cards you could potentially do card reading already. To do this you mix the cards randomly - actually you can make the person whose future or fortune you want to read mix them, especially if they know the meaning of the cards and positions unconsciously. Then you draw a card and place it in the first position. You could stop here to interpret it as is, I think it's better to keep on going as not to mix up your conscious and unconsciousness during the reading. So, place the cards in order until you're done without thinking too much about it. Once you're done the meaning of the cards should be taken into the context given by the position as well as within the context of the relationship between each other. (What does the present show? Does the challenge match the present?). Then the result of that can be presented in the context given by the person to further clarify possibilities and details.

Breaking the Tradition

Maybe you noticed it by the way I wrote this post. You are not required to pick existing cards or an existing system. You can actually make your own. The only important part here is that you need to familiarize yourself enough with the meanings of the cards and positions. It helps to assign certain directions to certain meanings. Like for example having a card placed higher could mean older age, in the future, later in life or maybe a superior thought, idea or body part. You can see in the Celtic cross tarot spread that the challenge is placed on top of the present. These types of symbolism play a huge role in the system you use to place your cards.

To prove this to you I'm gonna give you an example and tell a story in the next and last fortune-telling post of this on-going post-series.

^[1] https://en.wikipedia.org/wiki/Tarot
^[2] https://en.wikipedia.org/wiki/Major_Arcana
^[3] https://www.biddytarot.com/how-to-read-the-celtic-cross-tarot-spread/

Guild Wars 2: Fall Speed in Tyria

Since the post about the velocity in Guild Wars 2, I wanted to make one about the gravitation as well as the mount speed. Honestly, I just remembered the one about the mount speed while I started writing this haha! Anyways I sat down and sought a nice position to do my calculations.

Calculating Gravitation

There are a few ways to calculate gravitation. First things first we need to make ourselves clear that for our purposes gravitation is nothing more than a force that causes acceleration. One way to calculate acceleration is with the formula F = m * a. We don't know the weight or mass of our character nor if different races and character sizes play a role. Thus we need a different way. Another option would be
a = Δv / t. For this formula, we only need the velocity and the time. To get the velocity we can use the formula v = d * t. We can get the distance d using in-game measurements. For the time we can use a mobile phone or some other way to use a stopwatch. To get the velocity delta we need two spots, one with a long fall and one with a shorter fall or one that is long enough to perform two calculations on it.

Finding the Right Spot

An ideal spot would feature the following attributes:

• vertical wall
• nothing in the way during the fall
• easy to measure

I've decided to scout Divinity's Reach for spots and have decided for the one at the Plaza of Kormir and the other one is further up the Kormir High Road.

Guild Wars 2 Screenshot: Fall distance at Plaza of Kormir

Guild Wars 2 Screenshot: Fall at the Kormir High Road

Measuring the Walls

Guild Wars 2 Screenshot: Measuring Concept,
Plaza of Kormir

To measure the walls I used the skills and skill markers. Originally I've been using the Scourge Summon Meat Scepter- err I mean Flesh Worm is 1/4 of the staff mark and 1/3 of the shade radius. This means it has a 60 unit radius. The only issue that was left is that the indicators are a little bit off on some walls. The first wall took about one staff mark, one shade and half of the worm indicator. This is a fall of 480 + 360 + 43 = 883 units.
shades which feature a 180 unit radius and the staff trap skills which feature a 240 unit radius instead. Doing some experimentation I figured out that the indicator of the Summon Meat Scepter- er... Flesh Worm has a 60 units radius.

The second wall doesn't fit into a picture and was much harder to measure due to the marks disappearing after a certain time. It was 5 marks high and a little bit more than the Summon Flesh Worm indicator. This makes a distance of 480 * 5 + 120 + λ. For my calculations, I've set λ to 15. This gives me a distance of 480 * 5 + 120 + 15 = 2535 units.

Thought Process

If Tyria has gravity, the velocity at the longer fall should be higher than the velocity at the shorter fall. Both drops have a distance delta of 2535 - 883 = 1652 units. 

Possible Outcomes Include

a) The velocity of the first drop is significantly lower than the velocity of the longer second drop.

In this case there is an acceleration thus enabling us to further research. When we would do calculations on another planet or place in real life this would be the obvious result. In the case of game development games may not necessarily have acceleration and use a fixed fall speed.

b) The velocity of the first drop and the velocity of the longer second drop are similar enough.

There may always be errors in these empirical calculations. Errors during measurement specifically. Nonetheless if they're equal enough this means the falling speed is constant and the acceleration is strong enough to reach the terminal velocity in an instant.

c) The velocity of the first drop is significantly higher than the velocity of the longer second drop.

Honestly, I have no idea what's going on if this would be the case.

Measuring the Fall

 All we have to do at this point is to place our character, prepare the stopwatch and throw ourselves into our demise. Don't forget to start the stopwatch when the character starts to fall.

Due to the high chance of errors from reaction time I made 10 attempts. This table features all attempts and their resulting velocity in units.

Measurement	Short Drop (883 units)	Velocity (883 units)	Long Drop (2535 units)	Velocity (2535 units)
1.	0.97s	910.31u/s	2.51s	1009.96u/s
2.	0.91s	970.33u/s	2.39s	1060.67u/s
3.	0.97s	910.31u/s	2.53s	1001.98u/s
4.	0.87s	1014.94u/s	2.67s	949.44u/s
5.	0.88s	1076.83u/s	2.66s	953.01u/s
6.	0.82s	939.46u/s	2.62s	967.56u/s
7.	0.93s	949.46u/s	2.56s	990.23u/s
8.	0.96s	919.79u/s	2.67s	949.44u/s
9.	0.90s	981.11u/s	2.51s	1009.96u/s
10.	0.85s	1038.82u/s	2.61s	971.26u/s

Next up we take the average of the velocity which is 973.84u/s for 883 units and 986.35u/s for 2535 units. Now let's convert them to values that tell us more. For this, I'm using the same conversion I've used in all my posts. (1 unit = 2.52cm; 1 unit = 0.083ft)

883 unit velocity is

• 973.84u/s * 2.52cm/u = 2454.08cm/s which is 2454.08cm/s / 100 = 24.54m/s
• 973.84u/s * 0.083ft/u = 80.83ft/s

1260 unit velocity is

•  986.35u/s * 2.52cm/u = 2485.60cm/s which is 2485.60cm/s / 100 = 24.86m/s
• 986.35u/s * 0.083ft = 81.87ft/s.

Conclusion

I'm gonna call it a day here. The values seem to fall into either case a or case b. Now the question is whether or not it's a measurement error or if there is gravitation. Though if there is gravitation we can calculate it by finding a drop that's high enough on which we can do two separate time stops at two different points. That sounds difficult but it might work and even easier if done on video. So I'm gonna look into that in the next days. Until then.. stay tuned and maybe you find something else from me that's interesting. ^^

Fortune Telling: It Is a Delicate Thing [1/3]

Some guy or gal draws some cards puts them on the table and tells you something. That's what card reading is, right? Funnily real card reading or fortune-telling in itself is quite delicate.

Why Is It a Delicate Thing?

Telling the future shows one of the prominent features of magick as well as an issue. Let's start with the issue since it's easy for anyone to comprehend regardless of background.

Fortune Telling Issue

Before I can get into the issue we need to clarify the following. In this case, I'm gonna assume that destiny is not a fixed thing or can be changed in one or another way. If we assume that destiny is fixed, whether or not you do fortune-telling doesn't matter. Regardless of whether or not you do it, the outcome has already been determined and your decision to do or not do fortune-telling has been determined as well.

On the contrary, if destiny is not fixed this means the future has not been determined and fortune-telling changes the future. If we assume you do fortune telling to find something out about the future your new-found knowledge changes the future. The fallacy here is that you would have to do another session of fortune telling to determine the new future that was created by your first round. Despite your efforts, you would never be able to reach a state where you would actually know the future to a maximum of precision since there's always variability and the result changes with each attempt.

I mean.. you could make this into a super task if you have nothing else to do in your life...

Fortune Telling And Accuracy

You often hear people making fun over how inaccurate calls from fortune-telling people are. Hey, those who fake it even try to get the information out of you. There is a reason why it's done in fortune-telling. While a professional person may not even try to go into detail and to keep it vague they're not doing it because they want to, it's because of another principle of magick. The principle is similar to Heisenberg's uncertainty principle. To keep it short and simple: "The vaguer the statement is, the higher the chance of it being true.". This means we have either an inaccuracy of the statement or inaccuracy of its occurrence. The goal for a fortune teller at that point is to hit the sweet spot where you get the most accurate information at the highest chance of occurrence. While mathematically this may not seem too difficult to determine, there are still a ton of factors counting into it. Hence words should be chosen very carefully. When there are utensils like Tarot cards these utensils are kept vaguely as well. There are two reasons with one being the accuracy and the second being the compatibility of the utensil. The more meaning something has the more versatile it is when using it for magick.

Post-Post

Did you foresee the post of the post? Errr... anyways, this is one of a three-parter I'm gonna write. This one talks about foreseeing the future or fortune-telling in general. The next one will fixate on card reading and the last one will give an example of card reading with Magic: The Gathering cards.

Well.. at least giving an example on how it could be done. I need to mix something else into it in the meantime.... hmmm...