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Getting 2048 isn't worth of an impossible badge once you know the trick. Getting 65536 should be the impossible badge. (13172 is the actual highest possible number, but getting that is virtually impossible.)
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For anyone that just wants the badge and is having problems - left, down, right, down, left, down, right, down and so on. Press up once if forced and then carry on as before. You should easily be able to get the badge with it. And then you'll be hooked =)
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the highest tile possible is 131072 wich is supposely taking the corner point
then, its 16 spaces 131072 65536 32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 and then 4 and you wouldnt have another space to create one more four and double everything
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so far my record is the tile 16384, on my phone and its still ongoing but it takes a looooooot of time do double again
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BEcause of FemmeFatale, I managed to sintuple my score(5x is sintuple right?) So I find myself coming back to beat my high score, and to see how low I can get my score at beating the game.
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Alot of peoples solutions to getting a high score of 2048 or higher don't really work well... however this one does. It's basically foolproof. Start with Up, Right, Down, Left and repeat this pattern over and over again. You will easily get 2048 and higher.
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click up then right (or a variation) and repeat till you cant move then press left. You will eventually get 2048 or a really high score as this game has broken mechanics
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Got to 4096 only a few times, but I think an impossible badge for creating a 8192 tile wouldn't be unreasonable. I'd try.
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Threes clone, with a 'corner strategy' really broken. Just right, up until stuck. Then left and repeat. At least give you an 512