laitimes

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

Among the various puzzle games, "pushing the box" can be regarded as one of the most classic and well-known genres, somewhat similar to Minesweeper and Spider Solitaire. It's clean and crisp to play, there's no stress, and even people who don't know video games can have fun.

But perhaps because it's too classic, "pushing the box" is labeled casual, mild, fragmented, etc. in most people's minds, and they may spend a little time playing a few rounds on the commute, before going to bed after meals, and won't be particularly riveted to try to solve problems or achieve anything — or even mind the name of the game. From another perspective, the emphasis on casual and puzzle has also made many "push box" games similar in gameplay, and only the most imaginative innovations , such as Baba Is You — can impress.

Patrick's Parabox is an impressive game.

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

Isn't it "pushing the box"... Wait, can you still push it like that?

Brain-opening level design

"Patrick's Infinite Box Adventure" sells very cute and is very easy to get started. The player only needs to push the smiley face box and some other boxes that are the "protagonist" to the designated location, and you are done.

However, I soon discovered that the game wasn't as ordinary as it seemed. It does have all the elements of the classic "push box" game: some boxes, a "person" who pushes the box, and the basic law that if you accidentally push the box into the corner, you will fall into a dead end. But the game also introduces a concept of "nesting" – some chests can be nested into hollowed-out chests, and chests can also reach other places in very unexpected ways through scaling, mapping, and so on.

In other words, the various hollowed-out boxes and nesting mechanics are equivalent to expanding the original map several times, making the solution of this classic slider problem more complex and interesting. This kind of work that leverages a lot of creativity with a small idea is very admirable.

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

The nested relationship between the boxes is at the heart of the game's innovation

There are a total of 350 levels in the whole game, and each large chapter mainly promotes a way of playing, and the more you go, the more you open your mind. For example, you may use some hollow boxes to create a propulsion route that does not exist in the first place, or make the box enlarge and shrink, and "remotely control" some boxes to reach the designated location in synchronous nesting...

The developer of the game is Patrick Traynor, who has mentioned the source of the work's ideas in previous interviews. When Patrick was a member of the Game Development Club at the University of California, San Diego, he and his friends worked on a small demo in the game club, and the basic gameplay was also pushing boxes, but adding some stealth elements. After that, he made a model of a two-player game based on his original idea, in which one player controlled a character who was small and could walk through walls – after all, "stealth".

It wasn't long before Patrick temporarily lost interest in the project and shelved it. After more than 4 years, he found the original code again between the yin and yang and wanted to show it at a friend party. Coincidentally, another developer juner announced a push box game "Sokosoko" with multiple nesting elements in a Game Jam. Patrick was inspired and decided to continue with the idea, which eventually became what it is now.

Although the prototype of the idea was born very early, the game probably took Patrick more than two years of intensive development time. In his own social updates and interviews, Patrick mentions several important sources of inspiration. In addition to juner's games, there is the previous indie game Baba Is You, which is also known for its brain-burning, and another well-known "push box" game variant, Stephen's Sausage Roll.

First, let's talk about the older one. Stephen's Sausage Roll is a puzzle game released in 2016. The "chest" in the game is set as a sausage, and the player's goal is to roast all the sausages. To do this, the player must control the villain to push these sausages onto the grills scattered across the map.

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

Properly roasting sausages is a technical task

The puzzle difficulty of this game is that the sausage has two sides, each side must go through and can only go through the grill once, and if it is more than once, it will be burned and the game fails. At the same time, sausages generally occupy two compartments side by side, while grills come in a variety of shapes and sizes... So, strictly speaking, the sausage needs to be grilled not only two noodles, but 4 "noodles", or "lattice", and the player has a problem of how to make each noodle roll in the designated place in addition to the classic goal of "pushing the box to the designated location".

Believe me, the obstacles this little design adds to the player are incalculable.

In addition, in Stephen's Sausage Roll, villains can stand in any position and use a fork to move the sausage back and forth, left and right, rather than just pushing forward like the classic "push box" game. It is also possible to move multiple sausages at the same time in a reasonable position. With the help of ladders in the map, villains can also stand on sausages and other high platforms in the scene, and sausages can also be stacked between them - yes, this is a box push game with a three-dimensional map! It is up to you whether these mechanics are the "mercy" of the developers or whether they make the puzzle levels more complicated.

As another important inspiration for Patrick's Infinite Box Adventure, the 2019 release of the game Baba Is You looks more radical to the "push box" genre innovation. In the Steam comment area, many players can be seen saying that this game has made them doubt their own intelligence after playing it...

This feeling is all too normal, because Baba Is You turns the basic rules of the game into boxes - the "boxes" that need to be pushed in the game are actually squares with text written on them, and the squares have different functions depending on the text display, and pushing the "boxes" into different orders can change the rules of the game. In this way, the player's goal is no longer to honestly push the box from one place to another, but to directly "push" the nouns that make up the rules into a new order, forming new sentences to win the game. For example, changing the rule to "Baba Is Win" can pass the pass in situ. In the process of solving the puzzle, the "wall" and "rock" that originally constituted the obstacle can also be turned into other tools in this way, and auxiliary "boxes" such as "shift" and "flag" can help you find ways to adjust the order of words, etc. The form is very diverse, and the game mechanics are surprisingly flexible.

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

When the rules of the game also become boxes, the player may be at a loss like the protagonist of the little bunny

In terms of personal feelings, Baba is You is attractive enough for ordinary players like me, but some levels are really too difficult, and the game's difficulty curve is too steep and the lack of adaptation process is also a key feedback problem for many players. "Patrick's Infinite Box Adventure" does a better job in this regard, basically introducing a new mechanism in each chapter, teaching "hand in hand" for a while, gradually explaining the main gameplay of this chapter and then coming up with some comprehensive puzzles, so the overall difficulty curve is relatively smooth. This is not an easy task, Patrick also said in an interview, the difficulty curve is one of the biggest difficulties encountered in the design process, for friends to try many times before slowly settling.

Overall, though, none of these minor flaws prevented the games from being unique in their puzzle design, opening the door to new worlds for many players and developers.

When "puzzle" games meet math

Sokoban, the earliest "push box" game in history, was born in 1982 and was first released by the Japanese company Thinkin Rabbit. The game is a type of slider puzzle, and the original version had 10 classic levels and 10 evolved levels with hidden walls. In 1984, Thinking Rabbit launched the 50-level Warehouse Fan 2, followed by 1989's Warehouse Fan Perfect and 1991's Warehouse Fan Revenge, both of which had 306 levels each, somewhat similar to the episode.

The game was originally released on a very old home PC in Japan, and was later ported to other platforms and operating systems through the license of Thinking Rabbit, so a variety of different versions have been derived, including Game Boy, SFC, PS and mobile platform versions, but the game itself has not changed particularly much, and it can even be said that no official new works have been born, but there are more and more derivative and creative works.

Either way, the game itself and its core, which was imitated by its descendants, haven't changed much. The "Warehouse Fan" series basically laid the basic rules of most box pushing games since then, such as boxes can only be pushed and not pulled, and people cannot push two boxes at the same time. Of course, the details of these rules can be broken in the design of latecomers.

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

The ancient "Warehouse Fan" game already has the basic prototype of the "push box" game

So why has push boxing been so enduring, attracting generations of developers and players? The reason may be that although "pushing the box" is often used as a casual puzzle game, it is essentially a very complex problem, much more complex than it seems, and people are happy to overcome these difficulties to gain fun and satisfaction.

Just as all types of games have hardcore players who work tirelessly to explore possibilities and optimal solutions, the "push box" game has a loyal fan. In particular, many of the people who devote themselves to "pushing boxes" are math majors, especially those who focus on algorithms. If you search for "push box" on the Internet, you will find that a considerable number of results point to "automatic solution algorithm for push box games", "box push path search algorithm" and even "algorithm for determining whether there is a polynomial space for solving a push box level" and so on.

In fact, the complex nature of the seemingly simple and basic puzzle game of "pushing the box" has long attracted the attention of mathematicians.

How complex is this problem? On the page of Wikipedia's "push box" entry, you can see this description: "The complexity of the solution of the push box has been proved by mathematicians to reach the level of NP-hard, and later it has been proved that it is PSPACE complete." ”

Both of the seemingly technical terms in the description involve computational complexity theory. It doesn't matter if you can't understand it, the average person just needs to know that to use mathematical methods to prove that a push box level has a solution is one of the most difficult problems in this field. If you want to write a program to automatically solve a certain push box level, the amount of computation is also very large, and even quantum computers cannot solve it quickly...

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

Faced with the variables of the "push box" game, the human brain is better at processing than computers

A "push box" enthusiast, who is also a blogger in the field of mathematics, has written many blog posts specifically on related mathematical problems, such as "push box" level files and regular expressions, "push box" path search algorithm... He also found in practice that "we have held the MF8 (Rubik's Cube) 'Push Box' network competition for several years, and we have not yet seen anyone or organization that can quickly solve our main level of the game with a computer", and, "in practice, most of the push 'box' solvers use a lot of memory, often with the size of the 'push box' level grows exponentially."

At this point, the human brain may be more magical than a computer. Players often rely on intuition and logical thinking to solve the puzzles in the game, and enjoy the challenges in the process. For developers, this means that they have a large number of unrepeatable levels available, and they have a very large creative space in design. Adding a variety of variables to the classical mechanism makes it even more ever-changing.

Of course, this can also cause some difficulties. For example, "Baba Is You" has been updating the level for a long time, making small repairs, because players have launched routes that many developers have not expected in the process of actually playing, and some of them can easily lead to bugs in the level. The level editor is also a popular update among box pusher game enthusiasts, and the big guys have started to design a variety of wonderful puzzles.

Going back to Patrick's Infinite Chest Adventures, if there's anything in my opinion that makes it unique in its kind, it's probably the undisguised "Geek feel." The nesting mechanics in the game are bound to create a "matryoshka doll" effect at some point, and the two paradoxes of "infinity" and "infinitesimal" will appear in later levels. This means that it is very interesting for the player to push a box out of the existing nested box indefinitely in the game, or to push a box infinitely into the existing nested box. There are also tutorials on how to launch two paradoxes at the same time. This feeling is quite peculiar, as if I accidentally created some mysterious time and space in the game... Just like when I was a child, I always liked to stare at the infinitely extended space in two mirrors facing each other.

Patrick's Infinite Box Adventures: "Pushing Boxes" and Mathematical Adventures

In the game, it is sometimes possible to introduce a mysterious time and space where paradoxes coexist

These mechanics show the connection between the game and math on the surface, and with the cute art style and the fun of the level itself, it is a bit of a pleasure to show the meaning of "Geek's romance". Moreover, this romance is the icing on the cake, not at all high, and will not affect the ordinary players to pass the level; hardcore players can dig deep into these mechanisms, for example, on the B station, there is a video issued by the UP master of computational mathematics majors "How to play "push the box" with "set theory" knowledge", which feels like using theoretical knowledge to explain why various levels are so solved. In the comments section, many of my classmates began to enthusiastically discuss whether set theory was the most suitable for use in this game, which made me feel as if I had strayed into a mathematical interest group.

A surprisingly good example

All in all, I think the charm of the most ingenious and vital puzzle game lies not only in the creativity of the level itself, but also in this intellectual romance. You can feel something deeper behind it, you can get a glimpse of the mystery, but you don't need to be professional or smart to have fun, not to mention the very participatory and interactive element of the card editor.

Patrick's Infinite Chest Adventure is a great example of a surprise. It is in a sense a product of standing on the shoulders of giants, and before it, various developers have been adding bricks and tiles to the foundational game genre of "PushIng Boxes", but Patrick's Infinite Box Adventures still shows its own characteristics. I love the passion for the game that the developers show, and the wisdom they show in the process and results.

Will it be as big as Baba Is You in the future, or will it play any new tricks? There are no such signs yet, but it is always worth looking forward to.

Read on