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Eggsplaining the Number Train: An Eggstensive Guide to Cracking the "An Eggy Tally" Minigame

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Out of all the minigames released at the Trade Inn, this particular minigame is by far the most challenging, mathematically birdensome, and fun to solve, and from those I've talked to, many have a hard time getting to 7 eggs let alone the 12 you need to actually get the red bird icon reward. So I thought I'd make a guide detailing the strategy that I personally used to make it all the way to 12 eggs. Please note that this isn't a guide to maximize your score; it's a guide on maximizing your chances of "beating the game" by getting to 12 eggs for the final reward.

So to start off, I should explain for our purposes what this game is all about. 
- The goal of this game is to create as many fresh eggs on the board as possible, preferably up to 12
- Fresh eggs are ONLY made when you add tiles together that result in a value of EXACTLY 100 within the provided time limit; creating an egg after the timer expires will result in a rotten egg
- Every time you create an egg, fresh or rotten, the timer bar will reset
- You can only add tiles that are vertically and horizontally adjacent to each other; no diagonal tiles can be added
- You get to control which tile is adding and which tile is being added; the first square you click (which will be highlighted in green) is the square that will be added TO the second square you click, and the second square will be the one RECEIVING the 1st number.
- Any empty space that forms as a result of the addition will be filled in by gravity, resulting in a new number at the top of the column popping into existence on the board

Now let's dive into the strategy itself. I'll break this into parts so that the logic is easier to understand.

1. Where to Make Your Eggs

It's important to make sure that when you create your eggs, those eggs are located in the proper positions. Eggs that are made in terrible positions either block you from ever having access to that square or hurt your chances of executing the number-train method that I'll be covering in the section below.

For example, let's say you carelessly did something like this:
You can see that you've just blocked all chances of numbers above the eggs from reaching the row of numbers below the eggs. The only option you have at this point is to merge the numbers in the bottom row, resulting in something that looks like this:
Remember that diagonal addition is not allowed in this game. Now the bottom-left square has no way of accessing the rest of the board, and you've wasted an entire precious square of space. You need to fit 12 eggs on the board, so every piece of space counts!

What you want to do is eliminate the bottom-most rows first and work your way up. For me personally, this is the order I make the eggs:

2. The Number Train and Surface Area

This concept is the meat of what you need to understand to get far into the game WITHOUT relying on luck. Because you want to create a 100 at a SPECIFIC square (see section 1), it only makes sense that you want to plan ahead to make that 100. And because you're limited to only fusing numbers that are adjacent to each other, it only makes sense to have a specific trail (or a train) of numbers that you can follow to get to your 100 goal. The kicker here is that you can ALSO feed numbers adjacent to that train of numbers (i.e. on the "surface" of the train) onto the train itself to help you get to your 100 goal. Let me further explain with visuals.

Here, I have a situation where I'm trying to form the egg on the 3rd column, bottom row.


The green represents the number train. Right now, the number train's value is 38 + 29 + 14 = 81. Notice the numbers I've circled in red; these are the numbers I have directly available to feed into my number train to get to 100. 100 - 81 = 19, so I need ANY COMBINATION OF AVAILABLE NUMBERS on the surface of my number train to get to 19. You guys see any combination of numbers on the surface that can make 19? If so, I bet it was this one, and you'd be ABSOLUTELY RIGHT!


What you may have missed, however, was another possibility that you would only have realized if you expanded the number train to 4 squares:


You see the value of surface area, right? With this new 4-square number train valued at 88, you have 2 possibilities to make a 100 now because you INCREASED the surface area of your train by expanding that train WITHOUT going past 100. Increasing the size of your train increases the surface area, which ends up increasing the number of possible numbers you have at your disposal.

A word of caution, however; in a world where the timer doesn't exist, the best play would be to make the number train LARGE (while keeping the train's value below 100). Here's the problem though: the timer DOES exist. If you're a slow thinker like I am, you probably can't crunch the value of a 5 - 6-square train that might have large odd numbers, process the difference between that and 100 to get the value you need to add to the train, calculate all the possible combination of numbers you can make to find that value, move those numbers into the number train, AND finish the number train before the timer runs out. It's important to know your limits before you decide how long you want the number train to be. 

A final note regarding the number train: remember that gravity exists. If you try to add a number to a square above that number, the resulting square WILL fall down. Keep this in mind so that you don't accidentally destroy your number train. 

3. Low Numbers Good; High Numbers Bad

This part is pretty straightforward. You want as many low numbers below 10 as possible and as few high numbers above 10 as possible because (aside from the obvious idea that adding large numbers is generally harder) you can create a bunch of VIABLE numbers by adding small numbers together. You CAN'T make a bunch of viable numbers with large numbers, however, because you have a higher chance of overshooting 100. With 1's for example, you can make literally any integer in existence; with 2's, you can make 2, 4, 6, 8, 10, 12, etc.; but with 13's, all you can make are 13, 26, 39, 52, and other unholy large numbers that would most likely overshoot your number train past 100. Even if literally every number on the surface was too small for you to reach 100, keep in mind that every time your train eats a number, that number gets replaced, so you still have a whole bunch of chances to get the value you need.

4. Draw Out the Timer and Don't Give Up

It may be tempting to complete your egg the moment you see it, but I STRONGLY advise that you don't. Time is precious in this game, and with this number-crunching strategy, every second matters. Work on the next number train with the remaining time you have, but obviously focus your attention more on the timer than the 2nd number train. 

Finally, if you can't see any opening to finish the number train, it's important to NOT completely lose hope. As a last resort, you can "throw away" numbers on the surface of your train by merging them with a random number nearby until you get the number that you need.


5. The Strategy in Practice
Here is a GIF of what my general strategy looks like in practice:

So, step by step, this is what I'm doing and what's going through my head:
1. Okay, I see a path going towards the bottom-left square that has some high numbers. At a glance, it doesn't look like it's all that close to 100, so let's feed the train with other high numbers on the board, like that 16 on the upper-right square. 
2. Alright, so my number train running from the 2nd column 1st row square down to the bottom-left square is 36 + 8 + 19 + 4+ 7 = ? Maybe I should shorten the train so I can think more clearly.
3. Okay, so 44 + 19 + 4 + 7 = 63 + 11 = 74. I need to add 26 to the train somehow. Oh hey, there's a 6 above my train; if I'm gonna add it to the train anyways,  might as well just re-extend the train to the 6, so easy math: I need 20 now.
4. Oh hey, there's a 16 and 4 on my train: easy 20. Let's go ahead and add the numbers, but stop at the last addition.
5. Let's start working on the next number train while the timer continues.
6. Timer's almost out; let's finish the first train. 

I was able to record the exact game where I made it to the 12th egg if seeing an entire full game helps. It's good to keep in mind that you most likely won't immediately find an out every time, and that's fine. For me personally, the adrenaline rush of getting so close to the goal after failing multiple times tripped me up pretty hard, but if you're so far ahead, the last thing you want to do is let the bad morale from that mistake and previous mistakes get to you.

EDIT: Forgot a single sentence, and grammar

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