THE RUBIK’S CUBE MATH AND TUTORIAL – MAXIMUM NUMBER OF MOVES TO SOLVE CUBES WITH N SQUARES

The Rubik’s Cube is a 3D mechanical puzzle invented by the Hungarian architect Ernő Rubik in 1974.

Rubik's Cube

Rubik’s Cube

Its original and simpler version (3×3) – that presents 9 squares on each of the 6 faces, with 54 squares totally – can assume up to 43.252.003.274.489.856.000 positions!

Nonetheless, every position of 3×3 Rubik’s Cube can be solved in 20 moves or less (named “God’s Number”), whereas the maximum number of moves required to solve a Rubik’s cube with N squares per row is proportional to N2/log N.

These two results were found respectively by the cuber Tomas Rokicki and his colleagues in 2010 and by the Erik Demaine‘s (Professor of Computer science and engineering at MIT) research team in 2011.

Finally, I suggest you to watch this tutorial video which explains how to solve a Rubik’s Cube in under a minute.

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THANKS TO A 3D PRINTED BEAK A BALD EAGLE COMES BACK TO LIFE

In 2005 in Alaska, an adult female Bald Eagle was found, emaciated, without almost all of the right side of her beak, probably because of a poacher’s shot.
The eagle, called Beauty, was brought to Birds of Prey Northwest, a nonprofit organisation located near Coeur d’Alene (Idaho), where some volunteers nourished her daily, at first, with liquified food through a tube, and later, with solid food by forceps.

During this recovery time her beak didn’t grow back because the bone was too badly damaged. The raptor specialist Jane Fink Cantwell, refusing to euthanize Beauty, began to share the eagle’s story in order to attract the attention of scientists and specialists.

After hearing Beauty’s vicissitudes, the mechanical engineer Nate Calvin (founder of the Kinetic Engineering Group) was inspired and determined to help Jane.

The Beauty's beak before and after the implant

He made a mold of Beauty’s shattered upper mandible, laser-scanned it, fine-tuned it in a 3D modeling program, and created a prosthetic beak from a nylon-based polymer, using the so called 3D printing technology.

Computer model of Beauty's prosthetic upper mandible

With the help of researchers, engineers and medical specialists this prosthetic beak was implanted onto a titanium mount fitted onto the remaining part of eagle’s beak.

Thanks to the efforts of these many volunteers, from then on Beauty drinks water on her own and can feed herself and preen her feathers. Although, unfortunately, the prosthesis is not anchored securely enough to return Beauty to the wild.

This striking story – that join together love for animals and cutting edge technologies – has been told in the following video (shot and edited by Keith Bubach) which won the 2008 Emmy award:

Beauty and the Beak from Keith Bubach on Vimeo.