Number Merge · The puzzle notebook

In Number Merge, read the board after the move.

Compare two moves on one full board, count space after the spawn, and separate immediate score from room to continue.

A promising merge can still be a poor move. It may earn points while leaving the board cramped, scattering your largest tiles, or closing the route to the next useful pair. Before choosing a direction, picture the board after the slide but before the new random tile appears.

Read one line at a time

Sliding left first removes the gaps in each row. Equal adjacent numbers then merge in the direction of travel. Each resulting tile can merge only once during that move. These examples show the row before a move and the row afterward, excluding the newly spawned tile.

Slide left:
2  ·  2  4  →  4  4  ·  ·
2  2  2  2  →  4  4  ·  ·
4  4  8  ·  →  8  8  ·  ·
2  4  2  4  →  2  4  2  4

The third example does not turn directly into 16. The first two 4 tiles create a new 8, which has already used its merge for this move. On a subsequent left move, the pair of 8 tiles can combine. This distinction prevents a common planning error: expecting a whole cascade from one direction press.

Count space, not just points

A merge removes one occupied square, but a new tile appears after every changing move. If your move makes one merge, the spawn occupies one empty square, leaving the total number of empty squares unchanged. It can appear in any empty square, not necessarily the one the merge opened. Making two merges creates two spaces and then uses one, for a net gain of one empty square.

A slide without a merge changes positions but creates no space. If a new tile then appears, the board has one fewer empty square. Such moves can still be necessary, but you should know what rearrangement you are buying with that space.

Use a corner as an anchor

Pick a corner for the largest tile and try to build a descending sequence along its edge. If the largest tile is in the lower-left corner, a row such as 128, 64, 32, 16 gives the smaller numbers a clear direction to grow. Moving upward might pull that largest tile away and allow a small new tile to occupy its old position.

This is a practical preference, not an unbreakable rule. Sometimes the only legal move breaks the pattern. At other times, a temporary break makes a much larger merge possible. Read all four directions before deciding that the preferred corner must be protected at any cost.

Compare two moves on one full board

Use this constructed teaching position to compare Left and Up under our rules. It is a paper exercise, not a board-loading feature or a promise about the next random round. All sixteen squares are occupied. Work from the same starting position for each candidate; do not play Left and then treat that changed board as the starting point for Up.

64  64   4   8
 2   4   2   4
 2   8   2  16
 4   8   4   2

Left: a larger score, but no spare square after the spawn

The two 64 tiles merge into 128. No other row contains an equal adjacent pair. Before a new tile appears, the result is:

128   4   8   ·
  2   4   2   4
  2   8   2  16
  4   8   4   2

This adds 128 points through one merge. The only empty square is the top-right corner, so the new 2 or 4 must appear there. The board is full again: zero empty squares. A full board is not automatically game over. In this particular result, Up or Down can still merge tiles. Left and Right cannot change it, so those direction presses would add neither points nor a new tile.

Up: three smaller merges leave two empty squares

Read each column from the top. The first column merges 2 + 2 into 4; the second merges 8 + 8 into 16; the third merges 2 + 2 into 4. The fourth has no merge. Before the spawn, the result is:

64  64   4   8
 4   4   4   4
 4  16   4  16
 ·   ·   ·   2

The immediate gain is 4 + 16 + 4 = 24 points. Three merges create three empty squares. One new tile fills one of the first three squares in the bottom row, leaving two empty squares. This count holds whether the new tile is 2 or 4 and whichever of those three positions receives it.

The 64 pair in the top row also remains intact. Every possible spawn from this Up result is in the bottom row, so a following Left move can still combine the pair into 128. Up therefore preserves that immediate opportunity while making room. This is a reason to prefer Up for this exercise; it is not a proof of the best possible long-term score or a guarantee of reaching 2048.

Check the space budget after the random tile

  • Left: zero starting spaces + one merge − one spawn = zero spaces; 128 points now.
  • Up: zero starting spaces + three merges − one spawn = two spaces; 24 points now.

The score measures the values produced by merges. Space depends on how many merges occur, regardless of their values. Keeping those two measurements separate explains why the larger score can leave less room.

Why do four 4 tiles remain in the second row after Up instead of becoming 16?

Up combines tiles within columns, not across rows. The four 4 tiles end up side by side only after the upward move. On a subsequent Left move that row becomes 8, 8, empty, empty before the next spawn; it does not cascade into 16 during that same move.

On your own board, compare the number of merges, the position of the largest tiles, and the squares available for a spawn. Record the result before and after that one random addition. A board that looks open before the spawn may already be full when the turn actually ends.

Know the limit of prediction

You can predict the slide exactly. With several empty squares, the next tile can appear in different positions. With only one empty square, its location is known but its value is still uncertain. In this version, a new tile is 2 with 90% probability and 4 with 10% probability. Planning should allow for more than one spawn position. A strong-looking layout is an advantage, not a promise that the round will reach 2048.