Numbers Game – Numberama, Random Solution 1

Cn is column number, reading left to right.
Rn is row number, reading top to bottom.

Here is a random list.

There are a couple of ways to approach this puzzle. First, you could easily eliminate the 4 – 6 matching set, then proceed. However, I recognise a good opportunity to illustrate what I mean by ‘Seven is a Magic Number.’ There is an odd number of 9s, and it is possible to leave only one on the board before Checking.

Notice that it is possible to eliminate a 1 prior to the the 9 at C4R3. This can be done by eliminating the 1 – 1 vertical match at C5R2 – C5R3. If you can eliminate six other numbers prior to the target 9, then after checking you will have a vertical match of the 9 at C4R3. Since you can eliminate the other 1- 9 matching sets as well, this is a good strategy.


Now you have one blacked square prior to the 9 at C4R3. Eliminate 6 others, particularly the 1 – 9 matching sets.

I chose to eliminate the horizontally matching 5 – 5 because I noted that a 2 – 2 would appear beneath the remaining 9. This is an easy elimination, and will leave a vertical elimination of the remaining 9s. Note, you can determine this by simply counting where the numbers will go when you Check, or you can Check, Survey, Undo.

Now, you have seven blacked squares prior to the 9. When you Check, you will set up a vertical match.

As noted, you can eliminate the vertical block by eliminating the horizontal 2 – 2 matching pair. Do so, then eliminate the 9 – 9 matching pair.

Now you have eliminated the 9 – 9 matching set, which has made your task exponentially easier.

Next, focus on eliminating the 5 – 5 matching set. First, notice that if you eliminate the 6 – 4 vertical match at C6R2 – C6R3, you leave a 5 – 5 vertical match. Do this, then eliminate the obvious 5 – 5 horizontal matches.

With the 5 – 5 matching set eliminated, things have gotten even easier.

Next focus on the 3 – 3 set. Notice that between them are only 4 – 6 sets and 2 – 8 sets. Here is an important point:

If there is an odd number of those digits between the two you want to eliminate, you will have to eliminate one of them from outside the sequence between the pair you aim to eliminate. Also, sometimes it will not be possible to create a symmetric horizontal elimination, and you will have to look beyond the digits between the set in question (here the 3 – 3 set).

But here it’s straightforward. Eliminate the matching pairs until the 3 – 3 horizontal match remains. Then eliminate that.

Create the 6 – 4 sequence by eliminating the 2 – 8 vertical match at C2R2 – C2R3. The rest is obvious.

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