2048 puzzle

[rj]

Nice. I'm just happy I have half the community addicted to this. I'M NOT ALONE!

 

[ThomasJE]

Did you really get to 512 in 56 moves? Is that even possible?
20 for 32
37 for 64
82 for 128
155 for 256
196 for 256+128
230 for 256+128+64+32+16+8+4+2
270 for 256+128+128
311 for 512

It sounded to me like 56 was just a random number.

Also, is anyone else having problems with the mobile site? It's not working for me.

 

[brian724080]

Btw, 3D, 4D, and 5D

2048-3D is surprisingly easy:


Also:

 

[Rocky0701]

It sounded to me like 56 was just a random number.

Also, is anyone else having problems with the mobile site? It's not working for me.

Yes, 56 was just a random number, sorry for not clarifying. Or we could even do time competitions.

 

[Jaycee]

Sometimes I like to time how fast I can get a 128 tile. I've only done it under 10 times though; my best is 28.xx

 

[TDM]

Sometimes I like to time how fast I can get a 128 tile. I've only done it under 10 times though; my best is 28.xx

How do you time? I always lose a few seconds going from qqTimer to 2048 and back again...
E: incredibly lucky 31.50. Lost 5 seconds almost accidentally deleting a time clicking on the window...

 

[Rocky0701]

Just tried this and did an average of 5 timing to 128, and got 16.33 This was my first time trying this so i am pretty happy. I mostly just hit random keys, but there was still some strategy.

16.95 15.13 (14.02) 16.92 (18.27)

 

[Sajwo]

128 tile

Single: 5.61

Avg5: 7.57

(10.59), 8.11, 7.33, 7.27, (5.61)

Avg12: 8.28

8.11, 7.33, 7.27, (5.61), (10.04), 9.60, 8.35, 8.64, 8.40, 9.35, 6.82, 8.92

Easy. Just hit the buttons very fast and try to match big numbers

 

[Rocky0701]

256 tile average of 5: 25.99

(22.14) 26.74 (DNF: I got a game over) 26.69 24.54

New 128 tile average of 5: 11.33

11.59 (DNF) 9.45 12.96 8.32

 

[Sajwo]

256 tile average of 5: 25.99

(22.14) 26.74 (DNF: I got a game over) 26.69 24.54

This is impressive I have gotten like 8 DNF's in a row. But then I got 16.04 single

 

[TDM]

256: 22.58, 17.68, 19.13, DNF, 14.03 = 19.80

 

[Rocky0701]

64: 5.49 (7.49) 5.21 4.96 (4.06) average: 5.22

512: PB 52.32

 

[Sa967St]

Yay.

Spoiler

 

[Jaycee]

Would've been my 4th time beating it. All I had to do was connect the 32's and it would have the cascading effect from there.



Edit 2 hours later: I eventually got it. 4th win. Yay. I still haven't beat my original high score of 26xxx.

ANother edit 2 hours later: 5th win. This is getting good :3

 

[TheNextFeliks]

Ugh. 2nd 1024. Had 256 and 128 also. Changed forbidden keys halfway through on accident.


Edit:

YES!!!!!



Listening to the song Happy when this happened. Lol. Now I have stuff I can do.

 

[cmhardw]

We could also have little competitions on the lowest number of moves to get to certain numbers. Such as 56 moves to get to 512.

When you press an arrow key on the keyboard let's call that a "turn". When two tiles combine together to form the next tile in the sequence let's call that a "merge".

Let's take a rough look at how many turns it takes to create a tile.

To create the \( N \) tile, where N is a power of 2 greater than 2, takes \( \frac{N}{2}-1 \) merges as long as these are the merges tracking toward your goal tile.

For example you can create a 16 tile in 7 merges:
2+2=4 -> 1 merge
2+2=4 -> 1 merge
2+2=4 -> 1 merge
2+2=4 -> 1 merge
4+4=8 -> 1 merge
4+4=8 -> 1 merge
8+8=16 -> 1 merge

However, practically when you are taking turns you may make multiple 4 tiles but you only need to merge four of those 4 tiles to be two 8 tiles to make the 16 tile. If you count the merges for the two 8 tiles that did eventually become part of your 16 tile, then the 16 tile took you 7 merges to create. It's just that not all the merges you make are towards your goal. Counting only the merges towards you goal the above result would count the number of merges necessary to make the \( N \) tile.

Also, you can perform multiple merges in one turn. So, to get a 512 tile would take at least 255 merges. To do that in 56 turns would mean you would have to be averaging about 4 merges per turn I would say that 1.1 merges per turn is a rough approximation for a beginner, like me, at this game. Also, I may only be creating tiles at 90% efficiency (not every merge I make will create a tile that will work towards my goal of the 512 tile). So I would estimate that I might be able to make the 512 tile in:

\( \frac{\left(\frac{512}{2}-1\right)}{1.1*0.90} \approx 258 \) turns.

I don't have an empirical result for my tile creating efficiency here so I guess about 90%. I also don't know if I really am doing about 1.1 merges per turn but I would say it's a rough guess. I think this style thinking would be an approximate guess for the number of turns required to create a certain tile.

As a side note, to those who created the 2048 tile, did it take you around:

\( \frac{\left(\frac{2048}{2}-1\right)}{1.1*0.90} \approx 1033 \) turns?

I think that tile creating efficiency will likely be even higher than 90% and I also think that the average number of merges per turn could be as high a 1.3 to 1.5

Another guess at number of turns to create the 2048 tile could be:

\( \frac{\left(\frac{2048}{2}-1\right)}{1.5*0.95} \approx 718 \) turns.

For those who beat the game, do these numbers sound reasonable for the number of turns it took you to beat the game?

Btw, 3D, 4D, and 5D

2048-3D is surprisingly easy:
View attachment 3774

Wow, I really want to try 2048 3D now!

 

[cmhardw]

Yay.

Spoiler

Sarah, congrats! I haven't gotten the 2048 tile yet, but I really enjoy this game.

I would guess that you took approximately 1050 merges to beat this game. I got this by adding up the required number of merges for each tile on your board. Do you know about how many moves this solution took you? I'm trying to come up with an empirical result for the number of merges per turn on average that a person makes when playing this game.

If you made about 1.5 merges/turn then this game probably took you 700 turns? Does that sound reasonable?

 

[Jaycee]

Aaand here we go! Fantastic continuation on my 5th win. This is what the board looked like before my Game Over move.

View attachment 3784

So I actually got quite close to the 4096 tile! Most of the game, the 2048 was in the corner, but I had to hit the up key at one point. I still lasted quite a while after that, though! (I think I made the entire 512 with the 2048 out of the corner) I also smashed my high score, went from 26k to 34788.

 

[TDM]

I haven't gotten the 2048 tile yet, but I really enjoy this game.

Same... it's addictive. 1024 is so easy, but 2048 is impossible. I'll get there eventually!

 

[JTW2007]

For those who beat the game, do these numbers sound reasonable for the number of turns it took you to beat the game?

I haven't counted my turns yet, but at a guess I'd say these are underestimates for the method I've been using. I waste a lot of moves intentionally to avoid being stuck in a bad position on my turn, which means that, especially in the early stages of the game, I take lots of merge-free turns. I'd say due to this I probably average a little less than one merge per turn. I also end up with lots of high-value remnant tiles at the end of the game (Sarah: Your board has none of these; how did you avoid them?), so a non-negligible percentage of my merges don't go towards the 2048 tile. Other people's solutions may be much more efficient though, so perhaps ~1.1 merges/turn is a good overall estimate.

Is the code for the game available? It'd be cool to have the game track these statistics.