1. By Toby Cecchini, David Latt, Melissa Clark, Sam Sifton cooking.nytimes.com — The drink, invented by the New York bartender Sam Ross, who created the classic modern cocktail the penicillin, has slowly been gaining steam since it was introduced in 2007, showing.
2. The Cosmopolitan is a rose-tinted mixture of citrus vodka, triple sec, cranberry juice, and lime. In 1988 Toby Cecchini, a bartender at Tribeca’s famed Odeon, coined the cocktail informally called the Cosmo.
3. The Long Island Bar is a Brooklyn landmark, serving food and drinks for almost 55 years.

Toby Cecchini is an American bartender and author best known for inventing the Cosmopolitan. Originally from the American Midwest, Cecchini has been tending bar in New York City since the 1980s. While a bartender at Odeon, Cecchini created the Cosmopolitan, ushering in a new decade of contemporary urban cocktail drinking.

The Square-1, also known as Back to Square One and Cube 21, is a puzzle similar to the Rubik's Cube. Its distinguishing feature among the numerous Rubik's Cube variants is that it can change shape as it is twisted, due to the way it is cut, thus adding an extra level of challenge and difficulty. The Super Square One and Square Two puzzles have also been introduced. The Super Square One has two additional layers that can be scrambled and solved independently of the rest of the puzzle, and the Square Two has extra cuts made to the top and bottom layer, making the edge and corner wedges the same size.

History[edit]

The Square-1(full name 'Back to Square One') or alternatively, 'Cube 21', was invented by Karel Hršel and Vojtěch Kopský around 1990. Application for a Czechoslovak patent was filed on 8 November 1990, then filed as a 'priority document' on January 1, 1991. The patent was finally approved on 26 October 1992, with patent number CS277266 [3]. On March 16, 1993, the object itself was patented in the US with patent number US5,193,809 [4] then its design was also patented, on October 5, 1993, with patent number D340,093.

Description[edit]

The Square-1 consists of three layers. The upper and lower layers contain kite and triangular pieces. They are also called corner and edge pieces, respectively. There are all together 8 kite and 8 triangular pieces. The kite pieces are 60 degrees wide, while the triangular pieces are 30 degrees wide, relative to the center of the layer.

The middle layer contains two trapezoid pieces, which together may form an irregular hexagon or a square.

Each layer can be rotated freely, and if the boundaries of pieces in all layers line up, the puzzle can be twisted vertically, interchanging half of the top layer with half of the bottom. In this way, the pieces of the puzzle can be scrambled. Note that because the kite pieces are precisely twice the angular width of the triangular pieces, the two can be freely intermixed, with two triangular pieces taking the place of a single kite piece and vice versa. This leads to bizarre shape changes within the puzzle at any point.

For the puzzle to be in cube shape, the upper and lower layers must have alternating kite and triangular pieces, with 4 kite and 4 triangular pieces on each layer, and the middle layer must have a square shape. However, since only two shapes are possible for the middle layer, there is a quick sequence of twists which changes the shape of the middle layer from one to the other without touching the rest of the puzzle.

Once the puzzle has a cube shape, the upper and lower layers are cut in an Iron Cross-like fashion, or equivalently cut by two concentric (standard) crosses, that make an angle with each other.

Like Rubik's Cube, the pieces are colored. For the puzzle to be solved, not only does it need to be in cube shape, but each face of the cube must also have a uniform color. In its solved (or original) state, viewing the cube from the face with the word 'Square-1' printed on it, the colors are: white on top, green on the bottom, yellow in front, red on the left, orange on the right, and blue behind. Alternative versions of the Square-1 may have different color schemes.

Solutions[edit]

A good number of solutions for this puzzle exist on the Internet. Some solutions employ the classical layer-by-layer method, while other approaches include putting the corner pieces in place first, then the edge pieces, or vice versa. Some solutions are a combination of these approaches. Although these solutions use different approaches, most of them try to restore the cube shape of the puzzle first, regardless of the placement of the pieces and the parity of the middle layer, and then proceed to put the pieces in their correct places while preserving the cube shape. The shape is often restored first because it allows for the greatest range of possible moves at any one time – other shapes have fewer moves available.

The majority of solutions provide a large set of algorithms. These are sequences of turns and twists that will rearrange a small number of pieces while leaving the rest of the puzzle untouched. Examples include swapping two pieces, cycling through three pieces, etc. Larger scale algorithms are also possible, such as interchanging the top and bottom layers. Through the systematic use of these algorithms, the puzzle is gradually solved.

Like solutions of the Rubik's Cube, the solutions of Square-1 depend on the use of algorithms discovered either by trial and error, or by using computer searches. However, while solutions of Rubik's Cube rely on these algorithms more towards the end, they are heavily used throughout the course of solving the Square-1. This is because the uniform shape of the pieces in the Rubik's Cube allows one to focus on positioning a small subset of pieces while disregarding the rest, at least at the beginning of a solution. However, with the Square-1, the free intermixing of corner and edge pieces can sometimes cause a certain desired operation to be physically blocked; so one must take all pieces into account right from the beginning. Some solutions of the Square-1 rely solely on the use of algorithms.

Number of positions[edit]

If different rotations of a given permutation are counted only once while reflections are counted individually, there are 170 × 2 × 8! × 8! = 552,738,816,000 positions.

If both rotations and reflections are counted once only, the number of positions reduces to 15! ÷ 3 = 435,891,456,000. Also, it always can be solved in a maximum of 14 moves.^[1]

World records[edit]

The world record fastest Square-1 solve is 4.59 seconds, set by Martin Vædele Egdal of Denmark on 5 September 2020 at the Danish Championship 2020 in Roskilde, Denmark.^[2]

The world record average of 5 solves (excluding fastest and slowest) is 6.34 seconds, set by David Epstein of Australia on 10 April 2021 at Solving in Sale 2021 in Sale, Victoria, Australia, with the times of: (11.79) / 6.69 / (5.40) / 6.56 / 5.77.^[3]

Top 5 solvers by single solve^[2][edit]

Top 5 solvers by average of 5 solves^[3][edit]

Super Square One[edit]

The Super Square One is a 4-layer version of the Square-1. Just like the Square-1, it can adopt non-cubic shapes as it is twisted. As of 2009, it is sold by Uwe Mèffert in his puzzle shop, Meffert's.

It consists of 4 layers of 8 pieces, each surrounding a circular column which can be rotated along a perpendicular axis. This allows the pieces from the top and bottom layers and the middle two layers to be interchanged. Each layer consists of 8 movable pieces: 4 wider wedges and 4 narrower wedges. In the top and bottom layers, the wider pieces are the 'corner' pieces, and the narrower pieces are the 'edge pieces'. In the middle two layers, the wider pieces are the 'edge' pieces, and the narrower pieces are the 'face centers'. The wider pieces are exactly twice the angular width of the narrower pieces, so that two narrower pieces can fit in the place of one wider piece. Thus, they can be freely intermixed. This leads to the puzzle adopting a large variety of non-cubic shapes.

Solution[edit]

Despite its appearance, the Super Square One is not significantly more difficult to solve than the original Square-1. The middle layers are nearly identical to the top and bottom layers of the Square-1, and may be solved independently using the same methods as the Square-1. The edges of the middle layers are distinguishable because the edges with the same two colors are mirror images of each other, but the centers of each face are interchangeable since they show only one color each.

Square Two[edit]

The 'Square Two' is yet another variation of the popular Square-1 puzzle, with extra cuts on the top and bottom layers. It is also currently marketed by Meffert's online store.

The Square Two is mechanically the same as a Square-1, but the large corner wedges of the top and bottom layers are cut in half, effectively making the corner wedges as versatile as the edge wedges. This removes the locking issue present on the Square-1, which in many ways makes the Square Two easier to solve (and scramble) than its predecessor.

Solution[edit]

The Square Two, like the Super Square One, isn't much more difficult than the Square-1. In many ways, it's actually easier considering one can always make a slice turn regardless of the positions of the top and bottom layers. Mostly, it's solved just like the Original, merely requiring the extra step of combining the corner wedges. After that, it is solved exactly like the Square-1.

Toby Cecchini Coronavirus

Number of positions[edit]

There are a total of 24 wedge pieces on the puzzle.

Any permutation of the wedge pieces is possible, including even and odd permutations. This implies there are 24!=620,448,401,733,239,439,360,000 possible permutations of these pieces.

However, the middle layer has two possible orientations for each position, increasing the number of positions by a factor of 2.

This would theoretically yield a grand total of (24!)*2=1,240,896,803,466,478,878,720,000 possible positions for the puzzle, but since the layers have 12 different orientations for each position, some positions have been counted too many times this way. This reduces the number of positions by 12^2.

The final count is (24!)/72=8,617,338,912,961,658,880,000 total possible positions.

Toby Cecchini Boulevardier

See also[edit]

References[edit]

1. ^https://www.jaapsch.net/puzzles/square1.htm#numpos
2. ^ ^ab
3. ^ ^ab

External links[edit]

• (Back to) Square One / Cube 21 (With a program to solve Square-1)
• http://www.ganpuzzle.com/square1.htm Learn to Solve Square-1 with step by step animation accompanied by detailed descriptions.
• http://www.ganpuzzle.com/superSquare1.htm Learn to Solve Super Square-1 with step by step animation accompanied by detailed descriptions.

There is something perpetually boyish about bartender Toby Cecchini. It might have something to do with the curling thatch of hair that flops over his forehead. Or his round, wire spectacles, which give way to a signature look of wide-eyed naiveté. But then he says something like, “This place is such a spectacular shit-hole,” and destroys any greenness with a flourish of adjective-heavy wit.

Cecchini Style

White Negroni Sbagliato

Long Island Bar Gimlet

The Mess-cal

A native Midwesterner, Cecchini has tended bar in New York City since the 1980s and is credited with the creation of the Cosmopolitan. Though he treats the blush vodka drink (created at the Odeon in 1988, to be exact) like an albatross, there’s no denying his critical role in helping shape the identity of an entire decade of urban drinking. Cecchini went on to open the much-loved Chelsea bar Passerby, which was forced to shutter in 2008 after a decade in business. He’s finally reappeared—hair flopped, glasses perched—behind the counter at The Long Island Bar, his brand new watering hole built into a long-defunct, silver-sided diner on Atlantic Avenue in Brooklyn, only a few blocks from his Cobble Hill residence. Some nights he can be found in the back room rooting on the Greenbay Packers and drinking beer, and, on others, studiously taking orders and stirring Boulevardiers, quite at home in his new-old fashioned digs. —Leslie Pariseau

What do want to be when you grow up?
Certainly not an adult.

Best thing you ever drank:
A tiny dram of Delamain 1951 Cognac with my father on his deathbed.

Worst thing you ever drank:
Arguably the same as above.

First time you ever got drunk:
One day after tennis practice in high school, a friend and I set about very categorically to “get drunk,” not at all certain how exactly to effectuate that. His parents were out and we found a bottle of Tanqueray gin. We had no idea how to drink it, really, so we just poured enormous glasses of it warm into huge, ‘70s-era wine goblets and choked it down. The predictable technicolor bloodbath ensued.

If you had to listen to one album on loop, for the rest of your life, what would it be?
Wayne Newton’s Greatest Hits or Vanilla Ice’s To The Extreme? Alright, I’ll take Iggy Pop’s Lust For Life.

What’s the weirdest hobby you currently have or have had?
Walking train tracks. Literally. In high school I used to love to go on what I termed “linear walkabout,” wherein I’d walk for miles and miles balancing on one train rail without ever stepping off.

What do you know now that you wish you’d known five years ago?
How to make a perfect brandy crusta. I lied; I still don’t know that.

Weirdest cocktail experiment you’ve ever attempted:
I’ve been trying for years to make the perfect cocktail iteration of the dessert bananas foster. Its technical difficulty is perfectly paralleled by its profound dumbness.

What’s your favorite thing to do when you’re not eating, drinking or drink-making?
Modesty prevents my putting that in print, I’m afraid.

Weirdest drink request you’ve ever gotten:
A guy came into my bar and, without any prompting, asked me to make him a drink that was a mockup of a rabid polar bear wrestling a naked clown. I blinked, then made him repeat it, which he did, verbatim.

Your favorite bar, and why:
The Joynt in Eau Claire, Wisconsin.

Best meal you’ve ever had:
Krystal Burgers in New Orleans this past week. Oh, I’m sorry, you said the best?

What’s your go-to drink in a cocktail bar?
The Sidecar.

In a dive bar?
The Ramos Gin Fizz with smoked gin, elderflower tincture and quail egg.

Your preferred hangover recovery regime:
Don’t have dranked too much the night before.

The one thing you wish would disappear from drink lists forever:
Strawberries, oddly, because they may be my favorite fruit.

The last text message you sent:
“Sorry to mar your experience. How was the pasta?”