Category: 2048 strategy and maths

Your main objective is to create a tile with the number the 11th power of 2. This game has tiles with the same power of 2, which combine to and get the value of their sum.

Good luck! After reaching atyou can play more for gaining higher tiles. You have to obtain the highest number to be in a nice corner for easy access. So, pay attention to the edge of the grid.

2048 Strategy

Make the larger numbers around the corner and combine them when they match. If you made a higher number in the middle, you will find yourself lost inaccessible numbers and then you have to start a new game. Home Puzzle Controls k78 k75 k77 k Draw Climber Online. Play now. Love Balls 2. Wheely 5. Wheely 3. Escape Out. Cut the Rope Time Travel.

Wheely 6. Adam and Eve: Aliens. UNO Online. Brainy Cars. Unikitty: Rainbow Rage. Cut the Rope: Magic. Wheely 2. Sugar Heroes.I did it! After weeks of alienating efforts, I did it. I made it to the end of the tile game. At each stage, you slide tiles in any of the four directions of the screen up, down, left and right. Once tiles have slid and merged, a new tile pops up at a random free location of the grid.

The best way to get them is to actually play the game. In its basic version, the game stops as soon as you manage to create a tile.

2048 strategy and maths

But, as a nerdy mathematician, it sounds way too arbitrary to me. So, I tried to go as far as I could. And, a few days ago, after weeks of effort, I did it!

This means that, even in principle, you cannot go further than this. The game raised numerous intriguing questions about the underlying mathematics of the game. From induction to isomorphisms, including geometric sums, topology, probability and optimization, these mathematical questions are these I address in this article! What seems obvious still needs to be proved in mathematics! A simple proof is by mathematical induction.

To prove that all tiles are powers of 2 by mathematical induction, it suffices to prove two simpler points:.

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Point 1 fact is pretty straightforward. Indeed, at first, the only tile on the grid is the initial 2s or 4s we start with. And, as we all know it, 2 and 4 are powers of 2.

The Addictive Mathematics of the 2048 Tile Game

In point 2, we assume that at a given stage, all tiles are powers of 2. We need to show that no matter which move we then do, all tiles will still be powers of 2. The key to show that is to notice that all tiles that can be created in a move are either the randomly generated new tile or a tile obtained by combining two identical tiles. Yet, in the first case, we have see that tiles randomly generated are either 2 or 4 which are both powers of 2.

In the second case, the number of the newly generated tile is the sum of two identical tiles of the previous stage. Yet, we assumed that all tiles of the previous stage were powers of 2 this is known as the recursion hypothesis.

Namely, we now have a complete proof that all tiles are always powers of 2.

2048 strategy and maths

But before getting there, let me compute the sum of all tiles of that configuration. By combining 4 with our tile 4, we obtain a new tile 8. But then, this new tile 8 can be combined with the existing tile 8, hence creating a new tile 16… And so on.

2048 Math Game Free Strategy Guide / Walkthrough

How awesome is that? As it turns out, you can prove still by induction! Now, to prove that the configuration of the introduction is the mathematical end of the game, it suffices to show that the sum of tiles reaches its maximum in the configuration I got. Notice that, after every move, the total sum of tile numbers increases by the number of the new randomly-generated tile. This new tile is either 2 or 4. So, the total sum of tile numbers increases by steps of 2 or 4. It all has to do with the decompositions of these numbers as sums of powers of 2.

Indeed, otherwise, we can just combine 2 identical powers of 2 into their sum, hence yielding the same sum with one less tile. But do we have one tile of 2 and one tile of 4?The game is about adding two tiles together until you get the number Like most fun games, the concept of is deceptively simple, even a 5 year old kid could play it.

The 3 Top Priorities for game :. This is your top priority. This is your second priority. An example would be, The reason for Priority 1 is that this immensely increases your chances of successful merges of two higher numbers into 1. It synergises with Priority 3 to create a chain-effect. For example, imagine you have,64 on the top row. After merging another 64 with the 64 on the top row, you will have, And then, we have a ! Only press right when the upper row is full.

Press down only when you have utterly no other choice. Reason for Guideline 1: Pressing right when the upper row is not full has the chance of introducing a new tile on the upper left corner, so now your highest tile is no longer on the upper left corner. This is not good. Violates Priority 1. Reason for Guideline 3: After reaching the late game, we need to think a few steps in advance, and think of which is the best move in accordance to the Top 3 Priorities, and also can target the lowest tile on the upper row to set up a chain effect.

Just spam up and left until you get a moderately high number like or There is no harm done about this as the board is uncluttered and there is little chance of losing. You only need to start thinking deeper during the later part of the game, when your highest tile is or more. If no, it is better to quit and start a new game to save time. Same for Priority 2, if there is a 2 or 4 clogging the upper row, try a few more steps to see if you can salvage the situation, by merging to make a higher number.Account Options Sign in.

Top charts. New releases. Add to Wishlist. Join the numbers and get to the tile. But it is not the limit, you can do more after reaching in a tile.

This game supportsand more. Playing Math Puzzle Game Swipe to move the tiles. We can move tiles from left to right which will move all tiles rightwardsright to left, top to bottom and bottom to top. This version of supports auto save. Which will help you to save and continue your journey to that magic numberor even more. Playing is so easy, but most of time you loose this game by moving tiles in irregular directions thinking it will help to reach But a simple strategy will help to achieve in less than 20 minutes or even less.

Then move tiles right, left or bottom without moving biggest number. Don't ever move tiles to top direction. Always tighten the bottom row and join the tiles in this row without moving the biggest tile. Keep doing that and will help to reach Reviews Review policy and info. Smoother swiping and better tile movement.

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View details. Flag as inappropriate. Visit website.Be relaxed with this addictive mental math puzzle. Join the numbers and solve the math trouble as quick as possible to receive a high score. How to play — Large tile on the top left shows the mental math trouble. Game Features: — Gratis to play — Endless puzzles video test — Easy control — Subtle design Compete and beat your mates to be famed in the top of the leaderboard on Mini game Services!

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Professors React to 2048 - Numberphile

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Puzzle Game 2048

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Each visitor is able to add own tips, cheats and hacks, tricks and solutions for any mobie app. Write questions and wait for the answer from other players. No registration required! Share Your Guide. Describe your the best way to win the game, to get an advantage quickly and earn resources in the application as fast as possible.Last Updated: April 14, References. To create this article, 30 people, some anonymous, worked to edit and improve it over time. There are 10 references cited in this article, which can be found at the bottom of the page.

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2048 strategy and maths

Learn more It's simple to learn, but hard to beat. It is also available on retro consoles. You can play the game onlineor download it for iOS or Android. Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. Log in Facebook. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great.

By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article parts. Tips and Warnings. Related Articles. Part 1 of Swipe left and right several times optional. Start a new game, then swipe left and right rapidly. Continue until you have a couple rows of 2s, 4s, and 8s.

This isn't necessary to win, but it usually puts you in a good position and gets you to your first larger tiles faster. Build a higher tile in a corner. Combine the early tiles into a 16 or 32, and put it in a corner.

The goal of this method is to keep this tile in place for as long as possible, gradually building it higher and higher.The goal is to get a single tile to be Get two of the same numbers next to each other and add them together using your arrow keys.

Use the arrow keys to move your tiles in one direction or another. Take a break every now and then for food and water. Pick a corner - The goal is to make one tile The easiest way to do that is to pick a corner and focus on making that corner tile your highest number tile. Most people pick the bottom right corner, but you could pick whichever corner feels good to you.

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All of your biggest numbers should be in this row, from smallest to largest, to make it easier to merge tiles together. Try to always keep this row full of numbers even small ones so that you can move safely in three directions.

Stay organized! Focus on keeping your large numbers in the chain described above. You can keep the game going by keeping the number of larger numbers to a minimum and keeping the board full of smaller numbers instead. Plan ahead - Your game will last longer if you look a couple of steps ahead to plan your moves.

Try to make sure that a row or column with your largest number is always full or close to full of numbers. When new numbers appear, they are usually a 2 or 4. Think about where you need to combine numbers in order to keep your chain in order. All of the above strategies will only work if you take a minute to look ahead before you start merging your tiles. Copyright c Gabriele Cirulli. The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

Play the classic game of strategy. You can challenge the computer, a friend, or join a match against another online player. Outlast your opponents in the ultimate copter arena.

Grab upgrades and superpowers, avoid the toxic fog, and be the last one flying! Test your aim in online multiplayer! Race your opponent to get to zero first. You'll have to calculate your own score. Your pineapple is trapped at the top of a huge tower!

Jump over pits of lava and dodge dangerous traps to rescue it. Grow your civilization during the Bronze Age. In this strange and unusual world, you cannot jump. Fortunately, you CAN summon mountains beneath your feet.

And get filthy stinkin' rich. Let's get rolling! It may not look like much at first, but we have a feeling you'll be earning trillions of points in no time. Take your skills online and become world champion!

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