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VRChat is an enormous community where everyone can chat with each other in real-time, and if the user has enough equipment, he/she can perform complex actions and gestures, all in real-time. If you are a VRChat user, you may notice that there are some special objects in VRChat: Mirror, Video Players, and finally the most important of all: QVpens We all know that a pen can be used to write on a flat surface, it requires a medium to write on it, but this pen in VRChat requires nothing to write, all it needs is air. Yup, you can write on thin air. This tool is advantageous to users who have problems communicating verbally, maybe they are deaf, or they cannot talk, or maybe they have mic issues, or simply, they don't like to talk and like to write instead. And of course, if a QVpen can be used as a writing tool, then it is a drawing tool as well. Some users use VR sets and some users use Computers (yup, you don't exactly need a VR headset in order to communicate). Each with its pros and cons. For VR users, They can write normally simply using the controllers, the flow is smooth and handwriting is easier, most importantly this makes drawing much easier. The problem is they are going to have a hard time drawing something GEOMETRIC, for example, a perfect circle or a straight line. For Computer Users, It is hard for them to write or draw by using their mouse, the flow is rough unless they are extremely experienced, or you can lower the mouse sensitivity in the VRChat options But what is cool is users can use their keyboard to perform geometric movements, therefore they can draw geometric drawings. If you are a computer user, you Might want to know the controls of a QVpen (or any general pickup objects) : Left Click = Draw (pickup objects: maybe specified) Right Click = Drop (pickup objects: maybe specified) Scroll Wheel = Distance J = Rotate along UpDownAxis Clockwise from top L = Rotate along UpDownAxis Counter Clockwise from top K = Rotate along LeftRightAxis Backwards for upperpart I = Rotate along LeftRightAxis Forward for the upper part U = Rotate along FrontBackAxis Clockwise from behind O = Rotate along FrontBackAxis Counter Clockwise from behind Now since you know the controls, here are some ideas for you to refer to when you don't know what to draw: Straight Line Hold still your mouse and hold left click, and then move by using W/A/S/D Grid Hold your mouse still and you can combine WASD to get a nice "Ink surface" Grid Matrix just like drawing a straight line on a flat surface, you can use Jump or crouch (Z) to explore the 3rd dimension Circle Hold still your mouse and hold left click, and then press J/K/L/I/U/O or combined Geo Ring Sphere Hold your mouse still, and draw circles by using U/I/O/J/K/L which are parallel to each other Geo Chaotic Sphere Hold still your mouse and hold left click, and combine the following keys in any way: U,I,O,J,K,L Chaotic Sphere standstill, hold left click and then start drawing lines everywhere, the more the better, the messier the better. once you finished it, you are inside this "Chaotic Sphere" Verticle Cylinder standstill, hold left click and start pressing (J/K) and Z periodically, you will end up with a "Blender Cylinder" Horizontal Cylinder hold your mouse still, hold left lick, by combining drawing circles using U/O and lines using W/S, you can end up with a long cylinder Spiral Hold your mouse still, hold on left click, then press U/O and W/S at the same time, this will rotate the pen as you walk and draw. If you know your maths well, seeing this from the side is like a shifted sine graph. If your walking speed is too fast, you can crouch then draw the spiral instead. If you are a VRChat user, what will you draw usually on VRChat, tell us in the comment section below, if it is possible, screenshots can be attached.

If you still cannot understand the Mounty Hall Problem, or you came from TikTok, I hope that this post is helpful. Mounty what ? What is that ? If you still don't know what is the Mounty Hall Problem, read this section : A person presents you 3 boxes and tell you "one of them contains a Plush, and the rest of the two are completely empty (air molecules only), you can only choose one. And I know which box contains the Plush" And so you picked one of them, that person then opens another box, it is empty inside, and then he ask: "Would you like to change your choice before you lock your choice ?" Solution Maybe you met this kind of question before, and maybe you know that you should change your choice, but you don't know why. At the beginning, you might think that this has a 50% chance of getting the plush. But let's think it this way: Let's consider the four scenarios: Scenario A (Lock) (Fail) : You choose an empty box initially You lock your choice, you didn't get the Plush Scenario B (Lock) (Success): You choose a box with the Plush You lock your choice, you get the Plush Scenario C (Swap) (Success): you choose an empty box initially you swap your choice, the third box contains the plush. Scenario D (Swap) (Fail): You choose a box with the Plush you swap your choice, the third box is empty. What is the probability for each scenario to take place if you lock your choice? Scenario A (Lock) (Fail) : 2/3 (You start with an empty box) Scenario B (Lock) (Success) : 1/3 (You start with a Plush box) As you can see, if you lock your choice, you are most likely to fail. What is the probability for each scenario to take place if you change your choice? Scenario C (Swap) (Success) : 2/3 (You start with an empty box) Scenario D (Swap) (Fail) : 1/3 (You start with a Plush box) As you can see, if you change your choice, you are more likely to get the Plush. One thing : there is just a higher probability to get the plush if you change your choice, but not it is not DEFINITE. I hope this post helps, here's an image of a plush, good day (^w^)/ (any Vocaloid/MIKU fans here ?)

If you are here from Tiktok, nice; if you are here directly, this is the relevant link: https://vt.tiktok.com/ZSJNG1uC2/ Now, let us begin, Let's say we have an amount of money, say🍎 (if I use letters as variables, it could be messy and exhausting to identify between text and variable) then the table should be something like this: ┌───┬─────────┐ │spent│ left-over │ ├───┼─────────┤ │ 🥐 │ 🍎-🥐 │ │ 🌮 │ 🍎-🥐-🌮 │ │ 🥦 │ 🍎-🥐-🌮-🥦│ │ 🍋 │ 0$ │ └───┴─────────┘ notice that we used up all the money, therefore 🍋 must be equal to 🍎-🥐-🌮-🥦 in order to let Row4Column2 become $0 so let's sum up column 1 🥐+🌮+🥦+🍋 = 🥐+🌮+🥦+(🍎-🥐-🌮-🥦) = 🍎 and then let's sum up column 2 (🍎-🥐)+(🍎-🥐-🌮)+(🍎-🥐-🌮-🥦)+0$ = 🍎-🥐+🍎-🥐-🌮+🍎-🥐-🌮-🥦 = 3🍎 - 3🥐 - 2🌮 - 🥦 as you can see Column1 and Column 2 don't match up it is just a coincidence that when 🍎=50$,🥐=20$,🌮=15$,🥦=9$,🍋=6$, "amazingly", column2 = column1 + 1$ It is possible that there are other combinations such that Column2 is one more than Column1. since we know the criteria is column2 = column1 + 1$, then column2 = column1 + 1$ 3🍎 - 3🥐 - 2🌮 - 🥦 = 🍎 + 1$ 2🍎 - 3🥐 - 2🌮 - 🥦 = 1$ 2🍎 = 1$ + 3🥐 + 2🌮 + 🥦 🍎 = (1$ + 3🥐 + 2🌮 + 🥦) ÷ 2 as you can see we can simply assign a value to 🥐,🌮and🥦, we can then work out the value of 🍎. If you want 🍎 to be a whole number (not a fraction or a decimal), we have to make sure 1$ + 3🥐 + 2🌮 + 🥦 is divisible by 2 2🌮 is already even, so 🌮 can be any positive integer. if (🥐 is even) { then 3🥐is even and 1$ + 🥦 must be even, therefore 🥦 must be odd } else if (🥦 is even) {then 3🥐 + 1$ must be even, therefore 3🥐 must be odd, and 🥐 must be odd (because if 🥐 is even, 3🥐 would have been even and it will break the rule) } here are the 2 methods that we can assign the value to 🥐,🌮and🥦 such that 🍎is a whole number and Column1 + 1$ = Column2 : 🌮: any, 🥐: even, 🥦: odd OR 🌮: any, 🥐: odd, 🥦: even

Warning : DON'T SCROLL TOO FAST / EARLY IF YOU STILL WANT TO FIGURE THE ANSWER OUT YOURSELF Hi, if you are reading this, I expect you that you come from Facebook, if you are not, watch this video so you know what I am referring to in this post. https://www.facebook.com/johnnonnyofficial/videos/3949061975164324/ Hint 1 : Notice that the color of the couch changes, and so other objects / characters in the cards. Hint 2 : Only the physical objects / characters are permanent If you want to figure the answer out yourself, do not scroll down. If you want the answer or you want to check your answer, scroll down~ Answer in 3 2 1 Notice that each physical object/ character has a permanent color, which represents the "Correct color" Couch = Red Book = Blue Bottle = Green Mouse = Grey Ghost = White First Rule : If there is one item in the card matches its correct color, that item is the correct answer. Eg : If the bottle is green in the card, which is correct, the bottle is the answer. Second Rule : If there is an item with the wrong color, That item is not the answer and the physical item with that wrong color is not the answer. Eg : if the couch is blue in the card, the couch is not the answer, and the book(blue) is not the answer. It takes me to watch this video twice to figure this out ~ Share the riddle with your friends and see if they can figure it out~

Sometimes you might come across some questions or tasks or concepts. Sometimes, it is easy , sometimes it is hard. Sometimes you think that the given idea is easy, but to others, it is hard, and then you might think that the others are stupid. Sometimes you think that it is jumbled and complicated, but it is simple to the others, and you might think that they are intelligent. The truth is different people have their own methods to interpret and understand and memorize different ideas or tasks or concepts. Therefore, different people can deal with different topics or categories. Want some examples? Here are some: Someone asked me to find something on the shelve in Chinese (" 在厨上面“），and so I tried to find it on the upper layer ("上" has the meaning of "up"), but I could not find it, then he found what he needs On top of the shelve instead of in the upper layer... I tried to explain how does the Enigma Machine works to someone, to me, the mechanism is simple but interesting, but to others, the Enigma machine is a complicated mess. In a nutshell, different people have different methods or understanding to interpret, memorize, understand ideas, concepts, and tasks. So next time when someone doesn't understand you, can you understand what they know?

(art from "a name I keep changing aaa") Hi there. If you came from Youtube, I expected you have already watched "sneezing in different languages" by "a name I keep changing aaa" If you came here directly, go watch the video so you can understand what is going on: https://www.youtube.com/watch?v=r1CE0Hf_Vl4&lc=UgyzUfPjw1S_ye2kCMR4AaABAg.9KGFoa6WoLs9KJojc0NrPW Here are some of the translations for some of the Chinese phrases: Xiè Xiè 谢谢 Which means "Thank you" or "Thanks". Duì Bù Qĭ 对不起 Which means "Sorry", Obvious enough this is used for apologies, but here's a catch: the mistakes referred to by the apology are usually avoidable or intended. Bù Hăo Yì Sì 不好意思 Which means "Excuse me" This is also used for apologies, but instead, the mistakes are usually unavoidable or involuntary, or not intended. here are some extras : Ní Hăo 你好 the classic method to greet someone, this can be translated to "Hi" or "Hello" Dà Jiā Hăo 大家好 a method to greet a group of people or loads of audiences, "Da Jia" means “Everybody” or "Everyone" This whole phrase can be translated to "Hi everyone" Qĭng 请 This can be translated to "please", usually used for asking for help from someone. Duō Xìe 多谢 Has the same meaning as "Thanks you", but this time the "quantity" is much larger. "Duo" means "many" or "more". Zài Jiàn 再见 This can be translated to "Goodbye" or "See you" Bú Kè Qì 不客气 / Bú Yòng Kè Qì 不用客气 When someone thanked you, you can use this phrase, which can be translated to "You are welcome" Méi Guān Xī 没关系 You can use this phrase if you want to forgive someone, this phrase can be translated to "Never mind" I hope this is helpful full~ Share your thoughts or ideas in the comment section below~

1) Drizzle So little amount of raindrops that you don't even need an umbrella. Just like a spray~ nice and soft~ 2) Sprinkle Slightly heavier than a Drizzle, this can be used to describe snow as well. Just like sprinkling sugar on a cupcake. 3) Shower Ok, you can get wet with this, so you need an umbrella, although the duration is short. 4) Thunderstorm Raining heavily, and the area is enormous, you may hear thunders as well. Although it sounds scary, the duration is short. Pretty normal for countries around or at the equator. 5) Downpour Raining really heavily, and the duration is long. Just like you are pouring a bucket of water, CONTINUOUSLY~. This type of rain can be described by the idiom "raining cats and dogs" 6) Hail (in this case, this word is a noun.... not a verb...) The Solid-state of water, or known as ice, usually possesses the shape of a sphere or a cone. 7) Acid Rain When acid gas is absorbed by the water droplets in the sky, an acid rain may occur. Usually, the acid gasses are carbon dioxide produced from factories or vehicles.

Did you notice the big update of the Educational App : Math-FAST ? After a few feedbacks we have, we have decided to add new features and settings to the app, to make this app more flexible and available to every user. Why this app exists? Handling fast and simple calculations is one of the keys to conquer Maths, which helps us to reduce the duration of calculation and make things faster. When we were younger, we will calculate when we face a new operational question, say the first time when we met "2 + 3 = ?". Then we may use any reasonable methods to count, like using our fingers or counting 3 starting from 2, but this is too slow, that's is why we need to practice in order to remember "2 + 3 = 5" instead of counting it which costs a lot more time to do so. After several practices, we will remember the answer instead of calculating it for simple calculations, which makes things a lot faster and more efficient. Here are the 5 new features from the update. 1) Multiple Types for some of the Operations Theoretically, there are many ways that a question can be made, and yes, this app can generate questions with the same operations but with slightly different styles and looks. Different styles of questions can help users to deal with different types of questions even if the operation sign is the same. 2) Maximum & Minimum Now you can set the range of the numbers, say from 1 to 9, or 10 to 99, etc~ This means that this setting allows every user at different levels to use this app, from toddlers to elderlies. 3) 2 sets of Maximum & Minimum Now you can set the range for both of the numbers, This means that this setting allows every user at different levels to use this app, to practice different types of questions, from toddlers to elderlies. 4) Skip Enabled Originally, when you come across a wrongly answered question, the app will erase your answer and wait for your next answer, but if you really don't know the answer, you will get stuck until the time ends. Now with a flip of a switch, wrongly answered questions will be skipped, so that you can move on to the next question and waste no more time. But you might ask: "then how should I know whether I am correct or not ?", fear not, the solution will be stated in point number 4. 5) Adjustable Duration In the previous version of Math-FAST, the duration for each exercise is always 60 seconds, but to make things more flexible, now the users can set their preferred duration, say 1 hour 2 minutes and 3 seconds. Just be careful not to let yourself get into a marathon unless you really wanted to. 6) Show correct answer Just like the situation in point number 2, you will get stuck if your question is wrongly answered. Also with a switch, the correct answer will show up, giving the user a hint or reminder. This helps them to memorize the question and the correct answer. This feature is available ONLY if the switch in point number 2 is switched on. 7) Practice Report Originally, you are only able to see your Quantity Score and your Reaction Score. But this report will show all the important details when you finish your test/exercise/practice/or whatever ~ In this report, you can find: the list the chosen operation, the maximum number and the minimum number, the situation of the 2 switches in point 2 and 4, your Quantity Score, total answered questions, Accuracy, Total Reaction Score, Average Reaction Score, Average time, and the most important of all: the list of all wrongly answered questions, which is the solution to point number 2 So these are all the new features for this app, plus this feature (for now) is free for everyone. So go check it out, and share your high score ~ Let's see what you got ~ Have fun. And if you have any feedback or suggestions, feel free to share them with us so we can make this app better~

目前这里有两套口诀/诀窍/记法： - 化学元素周期表 1 至 31 - 金属活跃性顺序 ---===< 化学元素周期表 1(H) 至 31(Ga) >===--- 注：这个记法有3个部分：“山”，“故事1”，“故事2” 部分1：“山” | 01(H) 至 05(B) 山的左边是"H" 山的中间是“L” 山的右边是“B” 山腰是“e” 山顶是“i” 部分2：“故事1” | 06(C) 至 20(Ca) 那一天有生物实验，C同学顿时呐喊NO，原来她带的花朵 (Flower) 不见了。 ​ 最后同学只花了5秒钟就找到了花朵。 那位同学说 “Ne*……呐 (Na) …… 你的Marigold ,东西乱放~~~”，单单后面4个字就给她打击。​ C同学回家路上碎碎念 " Sí Pæ Sōi *" ，他万万没想到今天它会被同学这样嘲讽。 走到一半是 很不幸的被雷云(Cloud)的雷 劈到。 被雷劈，很不甘愿，“我要砍 (Kăn) 死你！我要卡 (Că) 死你！” ​ 【注释】 ​ Ne 在指示 物品的地方或方向时的日常用语。 例：“Ne…… 那个苹果在桌上。” ​ Sí Pæ Sōi 福建话，感慨自己有多么不幸， Sōi 是指“衰”，指“不幸、倒霉”。 “Sí Pæ”，原本指 “父亲死亡” ，后来指 “非常” ， 在这里，Sí Pæ Sōi 指“非常不幸” 注意+警告⚠ 由于这种句型含有诅咒的成分，在此不鼓励各位在日常对话中使用此句型。 部分3：“故事2” | 21(Sc) 至 31(Ga) 教官Scan 我们有没有剃 (Ti) 头发，凡(V)是没有的渴 (Cr)死我们。 我们就像猛 (Mn) 男一样，像铁 (Fe) 一样, 因为我们有 可可豆 (Coco beans) 和泥 (Ni) 巴。 用这些 出 (Cu) 去 炸 (Zhà -> Zn) 完他们的家 (Ga)。 ---===< 金属活跃性口诀 >===--- K, Na, Ca, Mg, Al, Zn, Fe, Sn, Pb, Cu, Hg, Ag, Pt, Au “文言文”：加拿大美女，新帖细签，同共 银铂金 “白话文”：加拿大的美女，新的帖子仔细签，和大家同共 财产（银铂金） 补充：若加入“氢”的话，顺序会是 K, Na, Ca, Mg, Al, Zn, Fe, Sn, Pb, H, Cu, Hg, Ag, Pt, Au

--< 1 >-- Counting the distance by using blocks in groups So far most players count the distance in Minecraft 1 by 1, it is quite dangerous if you miss a number. Instead of 1 by 1, you can try like 5 by 5 or 10 by 10. Eg: 10 planks, 10 leaves, 10 bricks, 5 planks, 3 leaves gives you a distance of 38 without counting the blocks 1 by 1. --< 2 >-- Locating the center of a square For most people, the first thing that comes to their mind is MAFS~ true, with Maths you can deal with rectangles. But for the squares, there is a shortcut that you don't need maths or counting during the finding of the center. Pick any corner and then start placing blocks to bisect the angle into two 45deg angles and continue until you reach somewhere close to the middle (you can extend it afterward if it is too short), then pick another angle (which is not the opposite angle) and do the same thing. The point where the 2 lines intersect is the center of the square. --< 3 >-- Locating the point where it is exactly under a specific Block of your choice Say you want to place a beacon right under a stained glass high up in the sky, how can you find exactly the point where to place the beacon? In Minecraft, although there are a bunch of floating blocks, Gravity is still working on some blocks, eg: sand, gravel, powders. These blocks will drop VERTICALLY if there is no block underneath them. We can use this feature to locate the beacon. Place a sand block or any Gravity True Blocks underneath your stain glass and let Gravity and the Block work for you, the place where the block lands is the location EXACALLY UNDERNEATH your target. PS: Ignited TNT is a Gravity True Block EXTRA : How about Locating a point where it is exactly above a specific block of your choice? --< 4 >-- Always make a backup for each period of time Backup your world folder seems boring but extremely important, when accidents happen, you still have a backup and you are still on track ~ If you are playing Minecraft on a Windows PC, to find your world folder, go to your File Explorer and type "%appdata%" in the directory bar, then go to "Roaming" and then you will find ".minecraft", click it. In the ".minecraft" folder, you will find a folder named "saves", which is the folder where all of your Minecraft worlds are stored. Get inside "saves", each folder is a world, you can zip up a folder at upload it to your cloud storage. To install a world, place the folder in the "saves" folder, then Minecraft will read the folders here. EXTRA:here are some interesting commands too: /give @p minecraft:item_frame{EntityTag:{Invisible:1b}} /give @p minecraft:debug_stick /give @p minecraft:tropical_fish_bucket{PersistenceRequired:1} If you have any other tips or hints, please share with us by typing them in the comment section below ~ PS: For number 3: We have just used a beacon, right?

During High school, we learned (or you will learn) that Ep = mgh where "Ep" is the Potential Energy (or Work that has to be done in order to reach that height), "m" is the mass of the object, "g" is the gravitational acceleration and "h" is the distance (or the height position). But this is only true when the distance is small enough such that "g" will be treated as a constant. During high school, we also know that g = GM/(r ²) where "G" is the Gravitational Constant, "M" is the mass of the other object and "r" is the distance from it. The further you get, the lower the value it has. As you can see the value of "g" changes as "r" changes. If the distance is extremely long, is Ep really = mgh ? "g" will change as "h" is changing during the process. In this case, we will have to use integral to solve this problem. Since we know that if "r" (or the distance) is small enough, "g" can be treated as a constant. And we know that Ep = mgh, so dEp = m g dr = (m)(GM/(r ²))(dr) where "dEp" is a small "piece" of the whole Work that has to be done or the Potential Energy it has, "dr" is a small "piece" or a small change of the whole distance. now let's start integrating: dEp = (m)(GM/(r²))(dr) ∫dEp = ∫(m)(GM/(r²))(dr) ∫dEp = GMm∫(1/(r²))(dr) say the starting position is "a" away from the massive object and the ending point is "b" away from the massive object, then we can get: ∫dEp = GMm[-1/r] Ep = GMm[(-1/b)-(-1/a)] Ep = GMm[(1/a)-(1/b)] Ep = GMm[(b-a)/ab] Conclusion: If the distance is short enough, we can use Ep = mgh, but if the distance is long enough, we will have to use Ep = GMm[(b-a)/(ab)] instead. EXTRA: Just looking at g = GM/(r ²) we know that the closer we get, the larger the value of "g". If we place an Apple so near to the core of the Earth, it should has a "g" approaching to an infinite amount.

Just with these two elements and a series of rules, questions can be discovered, and if we are careful enough, we can use them in our lives. Situation 1 : Mid-CheckPoint Here are the rules in this situation : 1) All the dots and lines must be drawn on a euclidean plane. (where all squares drawn on this plane has 4 right angles and all triangles have a sum of 180 degrees for their 3 angles). 2) you can only connect 2 dots with 1 line, after doing that, you must add a point on that line. 3) A dot can only have 3 line segments, maximum 4) No lines can cross, no dots can share the same location 5) A line can connect to the same dot Question: how many dots can be added when 8 dots are given at the beginning? Solution: In the beginning, you might start plotting 8 dots and try to draw as many steps as you can, but we can see things from the simplest form. Considering a dot as a single entity with a single property (location, in this case) is not enough... Let's try to imagine that now a dot as a room, with 3 doors, since all dots can have 3 line segments, maximum. We know that drawing a line will use up 2 doors, here, the number of doors decreases by 2. When we add a dot on a line, the line will past through 2 doors and one door will remain unused, here, the number of doors increases by 1. In conclusion, the number of doors will be decreased by 1 for each step. So in the given scenario, 8 dots are given, so there should be 8 x 3 = 24 doors, since it takes 23 times to subtract 1 to make 24 to become 1 (which is lower than 2 where it is the number of doors required for drawing a line), you can have 23 steps, and one door will remain unused, i.e. one dot will only have 2 line segments. Situation 2 : the Dot Web Here are the rules in this situation: 1) all lines and dots should stay on a euclidean plane. 2) 1 line only can connect 2 different dots, but a dot can be connected by several lines. 3) for simplicity's sake, no dots will share the same location. 4) lines can pass through other lines and dots Question: How many lines can be drawn if there are 16 points? Solution : You might start plotting 16 dots on a plane and start drawing lines. But before counting the lines, we can look for patterns without counting from 1 to a natural number... Let's start by plotting the dots in a flexible system: plotting dots D;1 to D;n where n is the number of dots we have (here, we use a semicolon to represent the index number, eg: "D;1" means "the dot with the index number 1" or known as "Dot number 1") for D;n, we can draw n-1 lines for n-1 dots ( number of dots - the dot itself = n - 1) for D;(n-1), we can draw n-1 -1 lines for n-1 -1 dots (since the line from D;n to D;(n-1) is drawn, we need the second "-1" to subtract) for D;(n-2), we can draw n-1 -2 lines for n-1 -2 dots (since D;n and D;(n-1) are connected to it, we need that "-2") for D;(n-3), we can draw n-1 -3 lines for n-1 -3 dots (since D;n , D;(n-1) and D;(n-2) are connected to it, we need that "-3") until you reach D;3, we can draw 2 lines for D;2 and D;1 (since all the dots where D;({x|x>3}) are connected to it already) and for D;2, 1 line can be drawn and for D;1, all dots are connected to it already, so no more lines can be added for D;1 (n-1)+(n-2)+(n-3)+(n-4)+...+4+3+2+1+0, where there are n terms since each term represents the lines added on that dot. With a little help from Sir Gauss, we know that the sum would be (0 + (n-1))n / 2 = (n-1)n/2 if there are 16 dots, then there should be (16-1)16/2 = 120 lines can be drawn. If you have other dots and lines questions, feel free to share it in the comment section below ~ or a new post could be cool as well ~