# Quick Links

If you’re looking for solutions to the standard layouts, use the links below. There are a couple of solutions to random layouts as well, illustrating the strategies outlined on this page. For each solution I provide step-by-step screenshots.

- Video of 1 – 18 Solution
- Introduction to Numbers Game – Numberama
- Numbers Game – Numberama 1 – 18 Solution
- Numbers Game – Numberama 1 – 19 Solution
- Numbers Game – Numberama, Random Solution 1
- Numbers Game – Numberama, Random 1000

# Terminology

Before we begin, we need to be able to talk about the game clearly. I will use the following terms:

**List**: the list is the stream of numbers on the screen reading from left to right, top to bottom, ignoring black space.**Black space**: when you eliminate a number, it is blacked out. This is black space, and it is ignored when the list is rewritten.**Sequence**: a sequence is a specific part of the list.**Matching-pair set**: this refers to all of the occurrences of add-to-ten numbers or identical matches in the list. For example, all the 3s and 7s are a*set*. If there are no 3s, then all the 7s are a*set*. The 5s are a set, and so on.**Head**: the head is the first number in the list.**Tail**: the tail is the final number in the list.**Eliminable**: a pair of numbers is eliminable (can be eliminated) when they are either the same number, or when they add to ten. For example, 2 – 8 is eliminable, as is 4 – 4.**Horizontal match**: a pair of numbers match horizontally when they are eliminable from left to right, ignoring black space.**Vertical match**: a pair of numbers match vertically when they are eliminable from top to bottom, ignoring black space.**Vertical block**: a pair of numbers is blocked vertically when a single, unmatching number appears between them vertically. Avoid this.

# Settings

Numbers Game – Numberama allows you to change the colours of the numbers. I recommend changing the colours to make it easier to spot matches. To do so, set 1 – 9 to the same colour; set 2 – 8 to the same colour; etc. For example, my setup is as follows:

- 1 – 9 blue
- 2 – 8 purple
- 3 – 7 green
- 4 – 6 red
- 5 black

If you set auto-clear, you will disrupt the possibility of undoing previous moves. Use this setting with caution.

# General Strategy

### Eliminate Matching-Pair Sets

Focus on eliminating one of the five matching-pair sets first. For example, survey the list and determine whether you can immediately eliminate all the 4 – 6 matches. If so, do so.

The game gets exponentially easier as you eliminate matching-pair sets.

### Retain Horizontal Matches

The temptation is to eliminate all the possible matches on the board, then Check. This is the worst strategy.

If you eliminate all horizontal and vertical matches, then after you Check, you rely *entirely* on vertical matches to continue eliminating numbers. This is bad. Judiciously retaining horizontal matches is key to solving the puzzle.

Consider: if you have 2 – 5 – 6 – 6 – 5 – 2, then eliminating the sixes leaves you with 2 – 5 – – – 5 – 2. Now you can eliminate the fives, then the twos. Creating, and often *retaining*, these kinds of sequences is a good strategy. It can be useful to *not* eliminate such sequences, depending on which vertical matches you aim to create — for example when implementing an XYX strategy (see below).

### Check, Survey, Undo

There is no penalty for checking then undoing. Use this to your advantage.

If your specific strategy calls for a vertical elimination, then it can be useful to Check, survey the list to determine how you might reposition numbers strategically, Undo, eliminate as necessary, then Check again to achieve your strategy.

If you need to move a number, say, two positions left, then undo the Check, eliminate two numbers at some point prior to the list position of interest, Check again, proceed.

It is trickier to eliminate an odd number of digits prior to a specific position in the list. Doing so requires at least one vertical elimination. ‘Seven is a Magic Number’ addresses this, and Random Solution 1 illustrates it.

### Give Up

If things have gotten out of control and you can’t make sense of the board and develop a strategy, then restart. There’s no shame in this. You will never improve your skills at recognising patterns and developing strategies while slogging through screens of seemingly endless matches. Eventually, as your skills improve, you will rarely feel the need to restart.

On the other hand, pure number elimination can be quite meditative. Proceed appropriately.

Generally, if I stop enjoying the puzzle, I restart.

I find that I can solve most given lists within a hundred matched pairs. When it gets to be significantly more, usually I will have retained a long sequence of horizontal matches as part of a strategy. Often a game will end for me with a matching Head and Tail (see below) and twenty or thirty of a repeated number in between. The only penalty for retaining long sequences is in your statistics. Let your ego guide your willingness to stick to such a strategy.

Most often, I give up when I recognise I’ve made an error — though sometimes I’ll doggedly pursue my mistakes to a few hundred extra matches to clear the board.

Also, I find that if I haven’t solved the puzzle in one sitting, I will have lost track of my strategy by the time I return. Restarting seems reasonable at that point.

# Specific Strategies

### Match the Head and the Tail

If the Head and the Tail match, and there are no other instances of that matching pair in between, then that pair is effectively eliminated. This is because when you Check, in the centre of the List will be a horizontal match of the Head-Tail pair. Eliminate it first, as appropriate, then proceed.

This is a good start to solving the classic 1 – 18 layout. Notice that you can vertically match the 1 – 1 pair at the Head, leaving 2 as the Head. This matches with the 8 at the Tail. The remaining 8 – 2 pair is separated by 9 – 1 – 1. Eliminate the middle 1 with the 1 below it, leaving the sequence 8 – 9 – 1 – 2. Then eliminate the remaining 9 – 1 horizontally. Eliminate those, and you are left with a 2 – 8 Head – Tail, effectively eliminating the 2 – 8 matching pair. (More on this later.)

Look for symmetry. If your list starts with the sequence 1 – 2, and ends with the sequence 2 – 1, then these four numbers will always be eliminable after you check.

### Seven is a Magic Number

When starting with a 1 – 18 list, or a random list in Quick Mode, you can, upon Checking, create a vertical match if you eliminate seven numbers prior to the number you want to match vertically. Note, in most cases you will leave a number in between the vertical match (a vertical block), so be sure that vertical-blocking number can be eliminated horizontally.

This can be useful if you can leave only one of a matching set before your first check. Then, after your first check, you can quickly eliminate the matching set. Again, this makes your task exponentially easier.

Notice that this technique depends on your having an odd number of members in one of the matching-pair sets on the initial board.

To review an illustration of this technique, see Numbers Game – Numberama, Random Solution 1.

### Create X – Y – X, Symmetric Sequences

Let’s say there are only two fives on the board, and they are separated by a two. That is, the only fives on the board appear in a sequence of 5 – 2 – 5. Assuming the two is exposed, a good strategy is to keep as many twos as you can on the board, then Check. Try to ensure that the rewritten 5 – 2 – 5 sequence is eliminable via a vertical elimination of the two, then a horizontal elimination of the fives.

(Note: if the two is above the second five, in this example, then it is blocked vertically. This spoils the XYX strategy; avoid vertical blocking.)

Continue until your Check allows you to eliminate all instances of the XYX sequence.

This can get complicated. If, after checking you are unable to eliminate one of the two XYX sequences, then after the next check, you will have four XYX sequences. Avoid this.

Furthermore, X – Y – Z – Y – X is a good sequence. In this case, aim to match the Z vertically.