Negg Sweeper
Can You Be a Grand Master?
by: docktor

This week: Neggsweeper

There have been several articles on Neggsweeper so far in the Neopian Times, and I certainly acknowledge and appreciate any previous authors whose thoughts I've duplicated here. (As they say, great minds think alike...)

For the single game scores, here's the list of ranking break points:

Amateur at 100
Novice at 200
Expert at 400
Master at 600
Grand Master at 800

Let's first concentrate on the logic required to solve the puzzles. The only difference among Easy, Medium, and Hard skill levels is the size of the grid and therefore the percentage of Neggs that are bombs. Here are some statistics:

For the Easy level, you get a 9x9 matrix, totaling 81 cells. Of the 81, 71 are "okay" and 10 are bombs. That means you have only 13% bombs.

For Medium, you have 119 of 144 (12x12) free, and 25 bombs, 17% of the board.

For Hard, there are 156 of 196 (14x14) and 40 bombs, which means 20% of the board is made up of bombs.

Obviously, the odds are better at Easy than at the other levels. But how important is that, really?

The real way to get a high score is not to play a difficult game, but to happen to hit the hidden prizes. Those prizes are as follows:

Fish Negg 500
Crystal Negg 300
Rainbow Negg 150
Purple Negg 100
Blue Negg 50

On Easy skill, you get 1 point for each space you clear, and if you clear more than 10 spaces at once you get a bonus equal to that number of spaces, effectively getting 2 points per space. On Medium you get double the cleared spaces as a bonus (3 times total), and in Hard you get triple, totaling 4 times the points.

You can hit more than one of the Negg prizes per game (even the Fish Neggs), so it's conceivable that you could get a very high score. But here's the tricky bit: you have to win that game. It doesn't matter how many extra points you get, if you end up at the end with a spot in which you must guess, you could lose it all.

And that's why I play most of my games on Easy. I know, "how pitiful," but then again I got my single game Grand Master playing on Medium. There's more below about playing on Easy in the part about cumulative totals.

I've played Hard many times, and it's more enjoyable sometimes as a brain teaser, but there's a good likelihood that I won't even be able to get a game going without a dozen or more tries. I only hit a bomb to start out about once in ten times on Easy, and can finish nearly every game without guessing. My high score on Easy is nearly 1000, which is a nice return on the 30 NP you have to pay to play a round.

Oh, well, I'm beginning to ramble here. Let's talk about strategy.

The key to solving Neggsweeper, in my opinion, is to focus on the 3x3 matrix around a cell you're working on. If the number in the center is a (1), and you already have 1 bomb marked, then you can just quickly clear the other 8 squares in that 3x3 block. Same applies if it's a (2) or other number: if you have that many bombs marked, clear the rest right away.

Corollary: if that number at the center of your block is equal to all the Neggs that exist in the block, they all must be bombs.

Let's try some specific scenarios you might come across...

Scenario 1: Two 2's at the end of a line

If you see (2)(2) at one end of a line, they're both bombs. The only way for the last (2) square to be a 2 is if the one next to it is a bomb too. Remember the 3x3 matrix:

| - - -
| 2 2 -
| a b c

The first (2) has an invisible column off the board to the left, which effectively reduces the block you have to deal with to 2x3 instead:

? | - - -
? | 2 2 -
? | a b c

It becomes immediately obvious that the two Neggs (a) and (b) must be bombs if you look at it this way. The second (2) points to the same two Neggs as the first one did, so you also now know that the third Negg (c) cannot be a bomb. If it were, then the second (2) would have to have been a (3):

| - - -
| 2 3 ?
| a b c

So now you've marked two bombs and cleared 9 spaces, just by knowing that (2)(2) at the edge means two bombs. But more importantly, we've explained how you can use the 3x3 matrix to help you.

Oh, and if the (2)(2) isn't by the wall but is still at the end of an edge, the same rule still applies. In this example, you can see that all the (2) spaces are guaranteed to be marking bombs next to them, including around the corner:

= = 2 2
= 0 a b 2
= = = c 2
= = = 0 =
= = = = =

The (2)(2) above (a) and (b) shows that (a) and (b) are bombs and the cell to the left of (a) can't be a bomb. Likewise the (2)'s to the right of (b) and (c) say that (b) and (c) are bombs, and the cell below (c) isn't.

Scenario 2: A corner

On to a few other immediately visible combinations. If you have a (1) at a corner with space around it, then you know that the Negg by it is a bomb:

- - - ?
- 1 = ?
- = a ?
? ? ? ?

In this scenario, the 3x3 matrix with the (1) in it contains only bomb (a), and all the other 8 cells must be empty. If the two cells marked with (=) in the diagram are also (1)'s, then you've just cleared six other cells:

- - - 0
- 1 1 0
- 1 a 0
0 0 0 ?

Because each of the 3 (1)'s has a 3x3 matrix only including (a). See how it goes? By the way, I've put (0) in each of those cleared cells, but they might have any number depending on what else is around. In any case, they're not bombs.

How about if there was another area too nearby to have a (1), but otherwise it was the same?

b - - ?
- 2 = ?
- = a ?
? ? ? ?

Exactly the same thing applies, since the (2) has only Neggs (a) and (b) in its matrix. Just proceed as though the (2) was the corner (1) in the example above and you'll be fine, other than making sure to mark (b) as a bomb, of course.

Scenario 3: Poking through the 2's

If you know that you have two bombs in a diagonal with a (2) between them, and there's a third Negg in the opposite corner, it's not a bomb. Okay, that one needs a diagram:

- = = =
- a ? =
- 2 b =
- - - =

(a) and (b) are known to be bombs, so the (?) cannot be. You've "poked through" the a-b diagonal from the 2 to a clear cell.

This is an extension of the matrix around the 2, but sometimes it's easier to go through and spot these easy ones on a sweep of the board. I usually go around quickly when the game gets started and mark all the corner Neggs. Often I'll end up marking two corners next to each other on a diagonal, so I can do the poke-through at the same time if the cell in between was a 2.

Scenario 4: That's all there is

If you get stuck with a guessing situation early on, just come back later and see if there's some logic based on how many Neggs are left to uncover that will help you solve that. Let's take this example, with 5 Neggs left to uncover (don't forget, that number up there above the board is remaining Neggs, not bombs).

What you see here is the remainder of the board at the end of a game, in the lower right corner:

- 1 1 2 1 1 |
- 1 a b c d |
- 1 f g h i |

You know that there are 5 Neggs and 3 bombs. Taking the cells individually, it's quite confusing. Starting at the right edge of the top numbers:

The (1) could be (c) or (d),
The next (1) to the left could be either (b) or (c) or (d).
The next (2) could be (a)(b) or (b)(c) or (a)(c)
The next (1) could be (a) or (b) and the left corner (1) could only be (a)

Aha! So, though several have different options, there is one that's a sure thing. Let's mark (a) as a bomb. Notice there is also a (1) next to (a) and (f). That means (f) is clear or one of them would have to have been a 2.

With (a) marked as a bomb, we know (b) is clear because there's a (1) over (a). So the (2) must be straddling (a)(c). Mark (c) as a bomb too, and therefore (d) is clear.

Let's see what this looks like now:

- 1 1 2 1 1 |
- 1 # 0 # 0 |
- 1 0 g h i |

We only have one bomb left, and it's one of (g)(h)(i). All we have to do is look at that cleared spot that was (f). If that's a (2) now, then (g) is a bomb. If it's not, (g) is clear and we click it and see if it's a (2). If so, (h) is the bomb, and if not, we're left with (i).

You could have seen that the clear space (d) was a (2) but you wouldn't have known if the other bomb was at (h) or (i), so it's best to come from the end with the most clear spots.

That last one was kind of complicated, but the purpose (if you could follow it--sorry if it got too confusing) was to show that slow methodical logic will get you through a lot of cases you might have seen as just a wild guess. You still have to guess sometimes though, so keep that lucky penny handy...

Cumulative Grand Master:

Not much to say here except that your only goal is to rack up 50,000 points. It's going to take a while no matter how you go about it, but it is pointless to try to get a lot of points and blow yourself up half the time. You're better off going for lower but quickly attained scores on Easy.

I've gotten over 900 on Easy (lucky, I admit) but can whip through a minimum of around 170 points in about a minute when the server's running fast even if I don't get any bonus Neggs. Even at half that rate, you'll get your Grand Master in less than 8 hours. If you spread it over ten days, you can rack up the daily maximum of 5000 NP too, less what you spend, of course, and probably only do it for 30-45 minutes each day.

Like I mentioned above, it's often hard to even start the Medium and Hard levels without hitting a bomb, and Easy is pretty consistent about clearing quickly. Tedious? Yeah, but so is refreshing the shops, and for that you don't get that cool "Grand Master" ranking :)
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