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How to Solve a Rubik's Cube in Only 23 Moves

I've never solved a Rubik's Cube. I'm that guy who takes the stickers off puts them where I want them in order to get it over with. (Much to the consternation of any legitimate puzzle-solver who might try to use my cube in the future.) So it was with some amazement that I learned that Rubik's Cube solutions are an area of active mathematical research. There are scholars out there working on ideal cube-solving algorithms, and major progress is being made towards "God's algorithm" -- more on that in a moment.

Math god Tom Rokicki recently proved that all possible Rubik's Cube configurations can be solved in 23 turns or fewer. In order to arrive at this conclusion he needed massive computing power -- the research was done on supercomputers at Sony Pictures Imageworks (in the idle time between rendering special effects for Hollywood movies). Rokicki's conclusion states that for any legal Rubik's Cube configuration, a solution exists in 21, 22, or 23 moves. (And a few special-case cube configurations may be solvable in 20 or fewer.) Now the trick is...what are those moves?

Rokicki's research is interesting in that it doesn't actually tell you specifically how to solve a given cube (contrary to my catchy blog title above) -- it just proves that a solution exists for all possible legal cube configurations, and that solution is guaranteed to be achievable in 23 moves or fewer.

This research is one step in a process that may arrive at "God's algorithm," a theoretically ideal solution to a puzzle. From Wikipedia's page on the algorithm to end all algorithms:

God's algorithm is a notion originating in discussions of ways to solve the Rubik's Cube puzzle, but which can also be applied to other combinatorial puzzles and mathematical games. It stands for any practical algorithm that produces a solution having the least possible number of moves, the idea being that an omniscient being would know an optimal step from any given configuration.

...It is unknown whether a practical God's algorithm exists for Rubik's Cube.

Further reading: Rokicki's paper on 25-move solutions, a nice Slashdot explanation of the implications of the research, more on God's algorithm, and a highly math-intensive page on Optimal solutions for Rubik's Cube.

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Stones, Bones, and Wrecks
3500-Year-Old Mummy Discovered in Forgotten Egyptian Tomb

As the site of the ancient city of Thebes, the modern-day Egyptian city of Luxor is filled with archaeological treasures. But until recently, two forgotten tombs—both located in the necropolis of Dra' Abu el-Naga, an important non-royal cemetery—hadn’t been fully explored. Now, National Geographic reports that experts have finally excavated these burial sites and discovered a 3500-year-old mummy, along with ornate funerary goods and colorful murals.

While excavating one of the two tombs, known as Kampp 150, experts found linen-wrapped remains that Egypt's Ministry of Antiquities believes belong to either "a person named Djehuty Mes, whose name was engraved on one of the walls ... [or] the scribe Maati, as his name and the name of his wife Mehi were inscribed on 50 funerary cones found in the tomb's rectangular chamber."

In addition to the mummy, archaeologists discovered wooden statues, masks, earthen pots, a cache of some 450 statuettes, and around 100 funerary cones—conical mud objects, which were often positioned outside a tomb's center, and could have served as identifying markers or as offerings—inside Kampp 150.

The Associated Press reported that the second tomb, known as Kampp 161, is thought to be approximately 3400 years old—about 100 years newer than its neighboring chamber—as its design is characteristic of other such structures dating back to the reigns of Amenhotep II and Thutmose IV.

Inside Kampp 161, archaeologists discovered wooden funerary masks, a decorated coffin, furniture shards, and the mural of a festival or party depicting the tomb's unknown resident and his wife receiving ceremonial offerings.

German scholar Friederike Kampp-Seyfried surveyed and numbered both tombs in the 1990s, which is how they got their names, but she did not fully excavate nor enter either one.

Officials celebrated the rediscovery of the tombs on Saturday, December 9, when they publicly announced the archaeological finds. They hope that discoveries like these will entice foreign travelers to visit Egypt, as political unrest has harmed the country's tourism industry in recent years.

“It’s truly an exceptional day,” Khaled al-Anani, Egypt's antiquities minister, said in a statement. “The 18th dynasty private tombs were already known. But it’s the first time" anyone's ever entered them.

Check out some pictures of the newly revealed relics below.

Mustafa al-Waziri, director general of Luxor's Antiquities, points at an ancient Egyptian mural found at the newly discovered 'Kampp 161' tomb at Draa Abul Naga necropolis.
Mustafa al-Waziri, director general of Luxor's Antiquities, points at an ancient Egyptian mural found at the newly discovered 'Kampp 161' tomb at Draa Abul Naga necropolis on the west Nile bank of the southern Egyptian city of Luxor, about 400 miles south of the capital Cairo, on December 9, 2017.
STRINGER/AFP/Getty Images

An Egyptian archaeological technician restores artifacts found at the newly discovered 'Kampp 161' tomb at Draa Abul Naga necropolis in Luxor, Egypt.
An Egyptian archaeological technician restores artifacts found at the newly discovered 'Kampp 161' tomb at Draa Abul Naga necropolis on the west Nile bank of the southern Egyptian city of Luxor, about 400 miles south of the capital Cairo, on December 9, 2017.
STRINGER/AFP/Getty Images

An Egyptian laborer stands next to an ancient Egyptian mural found at the newly discovered 'Kampp 161' tomb at Draa Abul Naga necropolis in Luxor, Egypt.
STRINGER/AFP/Getty Images

Ancient Egyptian wooden funerary masks and small statuettes found in and retrieved from the newly discovered 'Kampp 150' tomb at Draa Abul Naga necropolis in Luxor, Egypt.
A picture taken on December 9, 2017 shows ancient Egyptian wooden funerary masks and small statuettes found in and retrieved from the newly discovered 'Kampp 150' tomb at Draa Abul Naga necropolis on the west Nile bank of the southern Egyptian city of Luxor, about 400 miles south of the capital Cairo.
STRINGER/AFP/Getty Images

[h/t National Geographic]

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Kohske Takahashi, i-Perception (2017)
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Can You Figure Out This Newly Discovered Optical Illusion?
Kohske Takahashi, i-Perception (2017)
Kohske Takahashi, i-Perception (2017)

Ready to have your mind boggled? Take a look at the image above. What shape are the lines? Do they look like curves, or zigzags?

The image, spotted by Digg, is a new type of optical illusion published in the aptly named journal i-Perception. Discovered by Japanese psychologist Kohske Takahashi, it’s called the “curvature blindness illusion,” because—spoiler—the contrast of the lines against the gray background makes our eye see some of the lines as zigzags when, in fact, they’re all smooth curves.

The illusion relies on a few different factors, according to the three experiments Takahashi conducted. For it to work, the lines have to change contrast just at or after the peak of the curve, reversing the contrast against the background. You’ll notice that the zigzags only appear against the gray section of the background, and even against that gray background, not every line looks angled. The lines that look curvy change contrast midway between the peaks and the valleys of the line, whereas the lines that look like they contain sharp angles change contrast right at the peak and valley. The curve has to be relatively gentle, too.

Go ahead, stare at it for a while.

[h/t Digg]

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