We can also estimate how many moves it will take to get to this ultimate number. In 2048, tiles appear with values of either 2 or 4. This complicates our estimate a little since we don't know how many 2's and how many 4's have gone into making up a huge number. So let's take each of them separately to get upper and lower bounds for the number of moves required.

If we assume that all new tiles will be 2's, we can make an 8 tile with 2+2+2+2. So this will require 4 tiles, but only 3 moves, since each move adds two tiles together. For a 16 tile, it will be 2+2+2+2+2+2+2+2. We can make it a little clearer by using brackets for each tile: {[(2+2)+(2+2)]+[(2+2)+(2+2)]}. Counting the plus signs gives us 7 moves. It's pretty clear that to make a number *N, *we will need (*N*/2)-1 moves to make it, since each pair of tiles requires one plus sign between them. So that means if you're playing the 5×5 grid, you need to make 33,554,431 moves to max out the board using 2's!

We can make the same analysis using 4's: 8 = 4+4; 16 = 4+4+4+4; 32 = 4+4+4+4+4+4+4+4. Counting the plus signs again shows us that to make a number *N*, we need (*N*/4)-1 moves to make it with 4's. So, to max out the board with 4's would take 16,777,215 moves.

Now, remember 2's and 4's occur randomly. This means that there are multiple ways to make up each number, e.g. 16 = 2+2+2+2+4+4 or 2+2+4+4+4, etc. However, if we assume that 2's and 4's are equally likely to come up, we can just take the average of our two results to give us the real answer.

Therefore, the number of moves it would take for an actual game of 5×5 2048 to max out is *25,165,823*. To put that in context, if you could make one move every second, and you played non-stop, with no sleep, no mistakes and no breaks, it would take you **291 days, 6 hours, 30 minutes and 23 seconds** to max out the 5×5 board. For the 4×4 board, it's just under **13 hours and 40 minutes**, assuming no mistakes.