Problem 2265. 2048 Next Move

Created by Ned Gulley

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Given a board in the game 2048 (see the game here: <a href = "http://gabrielecirulli.github.io/2048/">2048</a>) and a direction ('up','down','left', or 'right'), move the game forward one turn.Move and merge blocks as required by the game's rules, but for simplicity do not insert a new 2.Example 1<pre> board = [ ...
 0 0 0 2
 0 0 4 4
 0 0 0 16
 0 0 0 16]
 dir = 'up'
 newBoard = [ ...
 0 0 4 2
 0 0 0 4
 0 0 0 32
 0 0 0 0 ]</pre>Example 2<pre> board = [ ...
 0 2 128 4
 0 16 4 32
 0 8 0 0
 0 0 2 0 ]
 dir = 'right'
 newBoard = [ ...
 0 2 128 4
 0 16 4 32
 0 0 0 8
 0 0 0 2 ]</pre>Example 3. Resolving AmbiguityIf we think of the directions as defining the pull of gravity, then we resolve ambiguous cases by first merging the two "lowest" blocks. See below.<pre> board = [ ...
 0 4 4 4
 4 4 4 0
 2 2 2 2
 0 0 0 0 ]
 dir = 'left'
 newBoard = [ ...
 8 4 0 0
 8 4 0 0
 4 4 0 0
 0 0 0 0 ]</pre>Inspired by a suggestion from <a href = "http://www.mathworks.com/matlabcentral/cody/players/17831-nicholas-howe">Nick Howe</a>.

Given a board in the game 2048 (see the game here: <http://gabrielecirulli.github.io/2048/ 2048>) and a direction ('up','down','left', or 'right'), move the game forward one turn.

Move and merge blocks as required by the game's rules, but for simplicity *do not* insert a new 2.

Example 1

board = [ ...
    0     0     0     2
    0     0     4     4
    0     0     0    16
    0     0     0    16]
 dir = 'up'
 newBoard = [ ...
    0     0     4     2
    0     0     0     4
    0     0     0    32
    0     0     0     0 ]

Example 2

board = [ ...
    0     2   128     4
    0    16     4    32
    0     8     0     0
    0     0     2     0 ]
 dir = 'right'
 newBoard = [ ...
    0     2   128     4
    0    16     4    32
    0     0     0     8
    0     0     0     2 ]

Example 3. Resolving Ambiguity

If we think of the directions as defining the pull of gravity, then we resolve ambiguous cases by first merging the two "lowest" blocks. See below.

board = [ ...
    0     4     4     4
    4     4     4     0
    2     2     2     2
    0     0     0     0 ]
 dir = 'left'
 newBoard = [ ...
    8     4     0     0
    8     4     0     0
    4     4     0     0
    0     0     0     0 ]

Inspired by a suggestion from <http://www.mathworks.com/matlabcentral/cody/players/17831-nicholas-howe Nick Howe>.

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Last Solution submitted on Dec 07, 2022

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Show 9 older comments

James on 1 Apr 2014

Anyone else ever get to the 4096 tile in the game? :-)

Ned Gulley on 2 Apr 2014

Nick Howe says he's done it, and now he's working on 8192.

James on 2 Apr 2014

Tell him to take a screenshot if he gets it!

Nicholas Howe on 2 Apr 2014

http://cs.smith.edu/~nhowe/export/8192.png

J.R.! Menzinger on 4 Apr 2014

what should happen if in a row is [0 4 4 4] and the next move is 'left'? and if the next move is 'right'?

these cases does not appear in the problem, but it can be interesting to test... ;-)

Ned Gulley on 4 Apr 2014

Good point! That complicates things nicely. I added a new example and corresponding test case that reflects my understanding of the 2048 rules.

Andrew Newell on 10 Jan 2015

I think it would also help to explicitly state that a block cannot be merged twice in the same move.

Jan Orwat on 2 Mar 2016

There is no assertion in test 4.

Ned Gulley on 3 Mar 2016

Thanks Jan! Fixed it. That test has been firing blanks for more than a year.

Jan Orwat on 3 Mar 2016

You are welcome. I wouldn't probably notice it if I had not sent an incorrect submission.

Jean-Marie Sainthillier on 9 Dec 2016

6 players like this wonderful problem. But at the same time 6 players like a problem like Problem 43033. Create a constant offset.
This is very confusing ...

Ned Gulley on 12 Dec 2016

I would love to find a way to get people "liking" problems more often. Liking makes the author feel good about a job well done, but more importantly it points people to good problems. Sometimes we try to motivate people to like problems. This happened with the October triathlon contest (when the problem you reference was created). But it can have an unintended outcome of encouraging people to like problems that aren't that great. The results are very uneven. Bottom line: if you like a problem, please "like" it!

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Solution 548104

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Paul Berglund on 19 Dec 2014

I too stole Tim's rotation code...

Solution 428262

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Michael Ryan on 7 Apr 2014

Using Tim's rotation code...

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Problem 2265. 2048 Next Move

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Problem 2265. 2048 Next Move

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