LOS ANGELES: Scientists created the world’s smallest noughts and crosses board using dynamic DNA origami tiles – microscopic organic structures that can be programmed to transform into predefined patterns.
The team at the California Institute of Technology in the United States had previously used DNA origami to create tiles that could be designed to self-assemble into larger nanostructures bearing predefined patterns.
They had chosen to make the world’s smallest version of the iconic painting by Italian polymath Leonardo da Vinci, Mona Lisa.
However, the technique had a limitation similar to that of da Vinci’s oil paintings: once the image was created, it could not be easily changed.
The team has now created more dynamic tiles, allowing researchers to reshape already-built DNA structures.
Using this technique, they created a microscopic tic-tac-toe game in which players place their X’s and O’s by adding special DNA tiles to the board.
“We have developed a mechanism to program the dynamic interactions between complex DNA nanostructures,” said Lulu Qian, assistant professor at Caltech.
“Using this mechanism, we have created the world’s smallest game board for playing noughts and crosses, where every movement involves molecular self-reconfiguration to swap hundreds of strands of DNA at a time,” Qian said.
Each strand of DNA is made up of a backbone and four types of molecules called bases. These bases – adenine, guanine, cytosine and thymine, abbreviated as A, T, C and G – can be organized in any order, the order representing information that can be used by cells, or in this case by nanomachines.
The second property of DNA that makes it useful for building nanostructures is that bases A, T, C and G have a natural tendency to pair with their counterparts.
However, a sequence can also pair with a partially corresponding sequence.
The other technology, self-assembling tiles, is designed to behave like the pieces of a puzzle. Each tile has its own place in the assembled image, and it only fits there.
In creating their new technology, the team endowed the self-assembling tiles with movement capabilities. The result is tiles that can find their designated place in a structure, and then kick out the tile that already occupies that position.
To start the tic-tac-toe game, Qian’s team mixed a solution of blank tiles in a test tube. Once the board is assembled, the players take turns adding X tiles or O tiles to the solution.
Due to the programmable nature of the DNA they are made of, the tiles were designed to slide into specific places on the board, replacing the blank tiles that were there.
An X tile could be designed to only slide in the lower left corner of the board, for example. Players could put an X or an O in any empty spot using tiles designed to go where they wanted.
After six days of engrossing play, Player X emerged victorious, researchers say.
The goal of the research is to use the technology to develop nanomachines that can be modified or repaired once they have already been built.
“When you have a flat tire, you will probably replace it instead of buying a new car. Such manual repair is not possible for nanoscale machines,” said Grigory Tikhomirov, senior postdoctoral researcher at Caltech. .
“But with this tile-moving process that we have discovered, it becomes possible to replace and upgrade several parts of nanoscale machines designed to make them more efficient and sophisticated,” Tikhomirov said.

Welcome to The Riddler. Each week, I propose problems related to the things that are dear to us here: math, logic, and probability. There are two types: Riddler Express for those of you who want something small and Riddler Classic for those of you in the slow motion of the puzzle. Submit a correct answer for either one, and you might get a shout out in next week’s column. If you need a clue or have a favorite puzzle to collect dust in your attic, find me on twitter.

Riddler Express

Chess fans like to claim that there are more chess sets possible than there are atoms in the universe. Well la di da. What about us tic-tac-toe enthusiasts? How many possible noughts and crosses are there for us?

Submit your response

Classic Riddler

From Tom Hanrahan, a variation of the classic:

You are about to play a game of noughts and crosses, with an advantage and a big disadvantage. The advantage is that you can start first. The downside is that you are blindfolded and therefore are not informed of your opponent’s movements.

It works as follows. The squares of the board are numbered from 1 to 9, as follows:

begin {matrix} nonumber 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 end {matrix}

You start by calling a number corresponding to the box in which you want your “X” to be placed. Your opponent then chooses a square for his “O”, but you don’t know which one. You continue like this, alternating turns. Each time you choose a square already occupied by your opponent, you are informed that the square is occupied, and you must then choose another one until you find an empty square.

Can you design a strategy where (just like in regular tic-tac-toe!) are you guaranteed to never lose?

Submit your response

Solution to previous Riddler Express

Congratulations to 👏 Harry Posner 👏 from Boston, winner of last week’s Riddler Express!

Last week we met Louie, who lived in a town where there was a 50% chance of rain every morning and a 40% independent chance every night. Louie went to and from work each day, bringing an umbrella with him if it was raining and not bringing one if it wasn’t raining. Sunday evening, two of his three umbrellas were with him at home and one was at his office. What were his chances of getting through the work week without getting wet?

The odds of Louie staying well dry were exactly 69.27%.

The author of this riddle, Josh Vandenham, suggested three ways to get the answer. The first is to proceed by brute force through all possible weather conditions, keeping track of Louie’s umbrellas in each case. There are two relevant times of day, for five days, and two things can happen at each of these points (rain or shine), so there are (2 ^ {10} = 1,024 ) weather patterns possible. It is a lot, of course, but not totally impossible.

The second is to narrow down the possibilities and keep track of the different “states” of Louie’s umbrellas. He could have three at home and zero at work, two at home and one at work, one at home and two at work, or zero at home and three at work. Only four states, which is not too complicated. The probability of each state can be seen in this overview of the Nate Langhinrichs solver spreadsheet.

By the time Louie arrives home on Friday night, there is a 30.73% chance that he has been caught in the rain without an umbrella, or 69.27% ​​that he has stayed dry.

The third way to solve is to generate computer-simulated weather and travel. Solver Lowell Vaughn, for example, took this approach and was kind enough to share your Python code.

Finally, another way to approach this problem would be with something called Markov chains – random event models, which use sophisticated linear algebra tricks like matrices. In this approach, the situation (the umbrellas) depends on the previous situation. This approach has been put to good use by the Aaron Cote solver. The movement through the random states (the work week) is described by a transition matrix, which contains the probabilities that the umbrellas move from one location to another on a given day. In our particular case, the matrix looks like this:

begin {pmatrix} nonumber 0.3 & 0.2 & 0.0 & 0.0 & 0.5
0.3 & 0.5 & 0.2 & 0.0 & 0.0
0.0 & 0.3 & 0.5 & 0.2 & 0.0
0.0 & 0.0 & 0.3 & 0.5 & 0.2
0.0 & 0.0 & 0.0 & 0.0 & 1.0 end {pmatrix}

In this solution, there are five states: zero, one, two or three umbrellas at home plus the state Louie has ever been wet in. The rows of the matrix are Louie’s current state and the columns are his destination. For example, he starts from the third row (two umbrellas at home). There is no chance that he will end up with zero umbrellas at home, there is 0.3 chance that he will end the day with only one at home, 0.5 chance with two at home, 0 , 2 luck with three at home, and no chance he will get wet this first day. To obtain the probabilities for the whole working week, it suffices to multiply this matrix by itself five times, representing the meteorological hazard occurring over the five days, which gives us this:

begin {pmatrix} nonumber 0.04791 & 0.07634 & 0.04976 & 0.01776 & 0.80823
0.11451 & 0.19889 & 0.15274 & 0.06752 & 0.46634
0.11196 & 0.2911 & 0.22553 & 0.12610 & 0.3073
0.05994 & 0.15192 & 0.18915 & 0.12425 & 0.47474
0 & 0 & 0 & 0 & 1 end {pmatrix}

Finally, let’s look at the third row (the state it started in) and the last column: It’s the chance that it gets wet during the week. Subtract from 1 to find the chance that it does not have get wet and you get 69.27%.

Overall, given the extremely rushed climate that Louie lives in, his Random Umbrella system doesn’t work too badly. TGIF.

Solution to previous Riddler Classic

Congratulations to 👏 Steve Altschuld 👏 of New Albany, Ohio, winner of the Riddler Classic last week!

Last week, seven anti-social settlers moved to a circular meadow with a radius of 1 mile, where they would temporarily overcome their anxieties to work together on building houses far from each other. Specifically, they wanted to maximize the average distance between each colonist and his nearest neighbor. With seven houses to build, it was pretty straightforward: one would build their house in the center of the circle, while the other six would form a regular hexagon along its circumference. Each settler would be exactly 1 mile from their nearest neighbor, so the average distance is 1 mile. But at the last minute, a particularly antisocial settler canceled his move to the prairie altogether, leaving just six settlers with homes to build. With fewer people, could they find a better arrangement? Could they increase the average distance to more than 1 mile?

Yes indeed they could. Specifically, they could increase the average distance from the nearest neighbor to about a huge 1.0023 miles! Ah, the great outdoors.

Here’s what the Optimal Antisocial Grasslands neighborhood looks like, courtesy of the authors of this puzzle, Randi Goldman and Zach Wissner-Gross.

Note that the “center” house is only a a little bit off-center. This is the key.

The particular case of six settlers is proving particularly tricky, as Randi and Zach explained: If there are two settlers, they will simply build houses at diametrically opposed points on the circumference. If there are three, four or five settlers, they will organize their houses in a regular polygon. If there are seven settlers, they will form a regular hexagon plus a settler in the center of the circle. But six is ​​different.

Our winner this week, Steve, explained how he started his resolution: With six settlers, you can place five houses on the circle and one in the middle. (If all six are on the circle, the best you can do is 1 mile away.) I placed the outer five houses where they would go if I created a hex without the bottom vertex. I then realized that I could move the central house north and south a bit and drag two pairs of houses – the two opposite pairs east-west around the circumference, one pair above the other pair – around the edge of the circle a little, in tandem. So now I have a formula with three variables: the distance between the central house and the upper house, the angle of the upper pair from the upper vertex, and the angle of the lower pair from the upper vertex. That would be a pretty awful equation, so I did what a lot of us do: I did it on a spreadsheet and toggle it until I got my answer.

Solver Laurent Lessard presented its “modeling and optimization” approach, in which he considers various methods to solve such optimization problems, including climbing, interior points, simulated annealing and the sound very cool particle swarms. He illustrated the optimal arrangements for this problem not only for six settlers but also for all numbers from two to 21 – from simple east-west separation to complex Ritz cracker.

This excellent solution has generated an interesting Twitter chat, in which mathematical collaborations have been proposed, additional optimization techniques have been suggested, and it has been underline that an entire area of ​​academic research was devoted to such questions with regard to electron crystals. Not only that, I was alerted to what has become my new favorite website: packomania.com. This is what you think it is.

Want more puzzles?

Well, are you unlucky? There is a whole book full of the best puzzles from this column and puzzles never seen before. It’s called “The Riddler”, and it’s in store now! Consider your vacation shopping done.

Would you like to submit a puzzle?

Email me at [email protected]

i played a lot of Tix.Tax on the sly recently. It’s a browser-based multiplayer game that takes the humble game of Tic Tac Toe to a new level. It’s the kind of game you might see playing in an episode of Star Trek alongside Five-Dimensional Chess or Go Upside Down.

In Tix.Tax, you play ten games of Tic Tac Toe at the same time. Each sector of the large 3×3 Tic Tac Toe grid is itself a small set of Tic Tac Toe. Once you win a small game, you take that space in the overall big game. You win the entire game if you win three small games in a row, as required by the laws of Tic Tac Toe.

When you take a seat in one of the tiny grids, the game moves to that area for your opponent’s turn. If I take the space at the top left in the central play, then my opponent takes a space in the top left play.

It is probably easier to show it.

The result is a tactical game of territory management where you try to force your opponent to play little games that are unnecessary for them, so that they have to hopefully give you the blow you want.

Tix.Tax gets complicated quite quickly. Importantly, if you take a space that would move the game to a small game that someone has already won, your opponent can play in any available space they like.

In the clip below, I know blue needs the space at the bottom right of the bottom right minigame to take that area. By taking this space, he claims this match. Since the game should then switch to the lower right game it just claimed, I can actually play anywhere I want. So I use my next move to win. Yay!

Yes, it’s pretty mind-blowing, but I really like it. The game is free and allows you to compete against people or a bot to practice. Fun fact: One of the creators is Jesper the End, one of the brains behind classic Minecraft adventure maps like Diversity.

What game is President Trump playing? By that I mean what’s real Game does he play?

Trump’s political performance, with seriousness and jest, has often been compared to failure. Even at Three-, four-, eight-, ten- and 12 dimensions chess. His supporters argue that he is a great teacher and his detractors argue that he is a patzer. CNN’s Chris Cillizza wrote two different articles accusing Trump of playing “zero dimensional chess,” whatever that means. Even Garry Kasparov, arguably the greatest chess player of all time, weighed in, to rise up against the use of this gaming snapshot via Politico.

In my job here at FiveThirtyEight, I spend a lot of time thinking about games – board games, video games, chess tournaments, math puzzles, international business game theory. So I understand that “playing chess” is an easy shortcut to “playing strategy” or “being smart” or whatever. But I think we can do better. I humbly suggest that Trump does not play chess (of any dimension), but rather something called “ultimate tic-tac-toe”. It’s time to update your tropes.

As fast as I can the rules: The ultimate tic-tac-toe, sometimes called a tic-tac-toe fractal or meta tic-tac-toe or tic-tac-tic-tac-toe-toe, is played on a three-by-three by three-by-three grid. three grids. It looks like this:

Each of the nine small sub-grids is a familiar game of noughts and crosses. Win the small game in one of these sub-grids and you can claim it with a big “X” or “O”, which counts as a square in your favor in the bigger game. Winning the bigger game is yours. ultimate goal – basically you want to win three noughts and crosses in the same column, diagonal, or row.

But here’s the catch: where your opponent moves dictates where you move, and vice versa.

For example, if I start by placing my X in the upper left corner of one of the small grids, then you need to place your next O somewhere in the upper left grid. Your game there then dictates the grid where I should make my next game, and so on.

(You can play the game for yourself here, as built by Vikesh Khanna.)

Playing a few games of the ultimate tic-tac-toe makes you feel in your guts what it’s like to be a keen observer of the past two years of news cycles. (I guess it sounds like this in the White House, too.) The ultimate tic-tac-toe is a superbly orderly distillation of the strategy of distraction, delay, misdirection, procrastination, and improvisation.

It is a game of the past and the present. While chess offers a singular goal – to capture the opponent’s king – the ultimate tic-tac-toe offers fluid and shifting goals. The latest events (Scott Pruitt) may feel very distant from past events that come back to the fore (Stormy Daniels).

The ultimate tic-tac-toe is a game of frustration. Good chess players develop a unique plan and try to bring it to fruition. Ultimate tic-tac-toe players cannot do this. A map (Infrastructure week) can quickly derail (Comey). The next plan (Infrastructure week) can quickly suffer a similar fate (resignation of an assistant).

Ultimate tic-tac-toe is a game of confusion. In chess, there is only one battleground. In the ultimate tic-tac-toe, there are plenty, both local and global. These battlefields interact with each other in strange and complicated ways. The locals, the residents (recurring fights on Twitter) have little immediately obvious relationship to the global relationship (the welfare of the American people).

The bottom line: even a good ultimate tic-tac-toe game seems hit and miss, easy, and even downright silly at first glance. There is no clear or elegant strategy.

None of this tic-tac-toe stuff is meant to lessen the intricacies or intricacies of the current political moment. Chess is known for its complexity, of course – there are more chess sets possible than atoms in the universe and so on. But the ultimate tic-tac-toe is not to be outdone. To obtain a very approximate upper bound of the number of possible games, we can imagine that there are 81 places for the first move, then 80 places for the second, then 79, then 78 and so on. This brings us to the number 81!, that is, approximately 6 followed by 120 zeros. It’s incomprehensibly large (and doesn’t even take into consideration the weird, complicated game game tree). Even computers Wrestle to play it well.

So is Trump playing his game right or wrong? I have no idea. All I really know is: it’s not chess. Please design your holds accordingly.

JERUSALEM: Scientists have developed a robotic system that can play tic tac toe, and that could be used to help stroke survivors improve their performance on real tasks in a fun way.
Researchers from Ben-Gurion University of the Negev (BGU), Israel, designed a game with a robotic arm to simulate “3D functional activities of daily living” – actions people take on a daily basis, such as drinking from a cup, which are often rehabilitated.
Designing a social robot to help rehabilitate a patient is a new field that requires a lot of research and experimentation to determine the optimal conditions.
“Playing Tic Tac Toe with a set of cups (instead of X and O) is an example of a game that can help rehabilitate an upper limb,” said Shelly Levy-Tzedek of BGU.
“A person can pick up and place a lot of cups while enjoying a game and improving their performance in a daily task,” said Levy-Tzedek.
For the study published in the journal Restorative Neurology and Neuroscience, researchers compared the motivation of study participants to play with a robot versus a set of computer-controlled LED lights to determine the importance of interacting with it. a real physical robot.
They tested the system on 62 healthy right-handed people in two age groups: 40 young adults around 25 (23 women and 17 men) and 22 people aged around 75 (10 women and 12 men).
Both groups preferred the robotic system to the LED lighting system. Older adults said it looked more like a human, while younger adults said the robot “was more interesting, fun and engaging.”
When asked which partner they would prefer to play two more games with, both groups chose the robotic system over the lights. However, when asked to play 10 more games, the older adults always preferred the robot, but the younger group preferred to play against the LED light system.
“Some of the young adults complained that the robot was moving too slowly; therefore, they preferred the faster system when asked to play a lot more games, ”said Levy-Tzedek.
“This indicates a need to customize the speed of the robot for each participant,” she said.
An unexpected discovery was that the robot’s movement influenced human movement. Young people and older adults moved much slower when playing with the slower robot compared to the faster lighting system.
These results indicate that people are ready to continue interacting with a robotic device in a social type setting, and this embodiment plays an important role, which is a positive sign for the future of such systems.
Now that they have established the feasibility, the researchers recommend testing their system on stroke rehabilitation.

Here’s a paradox: Some of the most popular and enduring games of all time get the least respect from serious gaming enthusiasts.

Consider a list from BoardGameGeek, whose members have cast millions of votes and ranked nearly 12,000 games. The lowest rated is the tic-tac-toe, followed by Chutes and Ladders, Bingo, War, and Candy Land. Parcheesi (19th worst) and Checkers (38th worst) are two of the oldest games people still play, having survived in various forms for at least 1,000 years. These games must have something going for them.

So what are geeks missing? Games are becoming popular for different reasons. Simplicity is one: playing Chutes and Ladders or Candy Land accustoms a child to taking turns, following rules and, if not the thrill of victory, certainly the agony of defeat. Of course, these games are completely random, making them non-starters for serious enthusiasts.

Tic-tac-toe adds a lesson in the importance of decision making and consequences – one wrong move and you lose. Its brevity makes it a perfect vehicle to illustrate the advantages of anticipating and taking into account the strategy of the opponent. And War introduces children to playing cards and their ranks, opening up a cornucopia of future games.

Things get more interesting when we reach the ninth game from the bottom: Monopoly, which has been around for over a century. Monopoly is neither simple nor random; it has several pages of rules and is full of social interactions and consequent decisions regarding the purchase, collection, exchange and management of resources (property and money). These same features are at the heart of modern top rated games. For its pioneering role in game design, pundits should love Monopoly, but they hate it.

Tic-tac-toe doesn’t have a lot of reps. Sure, it’s a brief, simple distraction from the monotony of existence, but once your 8-year-old self realizes that you can still force a draw, it loses its appeal. The problem with noughts and crosses is the lack of strategic depth: there is only one viable strategy, and this strategy is simple enough to be memorized and applied with almost no effort. So the noughts and crosses falls into the sad category of solved games. It would be more unpredictable to challenge someone to recite the alphabet backwards.

Many other games with oft-lamented design flaws have it worse. Monopoly – the great lady of vilified games – leaves any meaningful strategy at the door and entrusts its players to a five-hour demonstration of the evils of the unbridled real estate markets. Pick Candyland, Sorry !, and their ilk looks cheap. They’ve been through enough abuse already.

Yet even with his ignominy at the bottom of the Geek board game rankings, the tic-tac-toe can be redeemed with three simple tricks that turn it from a trivial exercise into a much deeper and more enjoyable game. Note that this new version is still a resolute game, but the winning strategy is more complicated than in the vanilla tic-tac-toe, and therefore more difficult to memorize and deploy. And, most importantly, your next opponent will not yet have practiced the strategies necessary to win.

Numerophile has a video in which mathematician Thane Plambeck discusses this variation on the noughts and crosses, in its one- and three-board versions. Plambeck wrote an article about the game you can find on arXiv.

The first twist of this new version of the noughts and crosses (available in the Apple Store under Notakto) is this both players play as X. Normally, of course, one player plays as X and the other as O, and they go head-to-head to make three in a row. If both players play as X and neither of the other rules change, the game is still a draw. Instead of a draw, the first player can still force a win.

To solve this problem, we adopt another rule change known as misery play, in which the way to win is to lose. It still doesn’t make the game much more interesting. Your third and final twist will correct this: play on several boards at the same time. If three X’s appear in a row, that board is dead. The game continues until there is only one board left. Whoever makes three in a row on the final board loses the game.

Even those tweaks on a game as simple as noughts and crosses should get you started. But watch Plambeck show off his work below, to get the full effect. “This game is difficult to master,” he says. It was about time, noughts and crosses.