Math Games

Nob Yoshigahara

Ed Pegg Jr., June 28, 2004

In 1984, a small group of puzzle collectors met in Hollywood.  As the festivities got underway, the attendees were shown a very large Rubik's Cube puzzle.  Suddenly, out of it popped Nob Yoshigahara, a famous puzzle columnist from Japan.  He had puzzles for everyone, as always, some magic tricks, and plenty of jokes.

The son of an electrical engineer, Nobuyuki Yoshigahara was born on May 27, 1936.  He grew disenchanted with his first career as a chemist after getting caught in an explosion, and became a teacher of mathematics.  Nob wrote columns, too, many of them.  At one point, he wrote 17 puzzle columns a month.  Also, he was the world master of puzzle mechanisms.  When the 4x4x4 Rubik's Revenge had a problem with fragility, Nob found an improved mechanism, and passed it on to the puzzle manufacturers, which they subsequently used.

Rubik's Revenge
Figure 1. Rubik's Revenge (available from Mefferts puzzles).

From the back blurb of Rush Hour:  "Nob Yoshigahara is a celebrated inventor, collector, and popularizer of puzzles, one of the best the world has ever seen. He has written some 70 books on puzzles, has monthly columns in several popular magazines including Quark, and has participated in international puzzle parties all over the world. You will find his best work contained in Rush Hour ... and in the diabolical elegance of the puzzle play in each of the forty challenge cards." For Binary Arts (AKA Thinkfun), Nob invented or helped with Shape by Shape, Hoppers, FlipIt, and Lunar Lockout.  Each of the puzzles was analyzed by his crack team of puzzle geniuses, the NoBrainers. Earlier this month, Bill Ritchie, the owner of Binary Arts, received yet another new puzzle from Nob.

Rush Hour
Figure 2. Rush Hour (available from Binary Arts)

Nob adds one puzzle:  "According to normal RUSH HOUR rule, your car XX must go out from this garage through the exit (=>). Only one exception for this problem is, you can remove one car. Which car should be removed to let your car go out? Do not remove the XX itself.� Find its shortest moves."

|OBXXEF => exit

Nob relentlessly promoted puzzles worldwide.  For Ishi Press, Nob developed a series of beautiful glass puzzles.

Aspargus Orange Pineapple
Figure 3. Three of Nob's Glass puzzles (Puzzleworld)

Also earlier this month, he helped Scott Kim with a new Bogglers column for Discover magazine -- highlighting a few of the puzzles from Nob's latest book: Puzzles 101: A Puzzlemaster's Challenge.  Nob helped Scott with many puzzles.  Nob helped me with many puzzles, and greatly aided my site and columns. When I was unemployed, and didn't do well at a puzzle convention, he bought all my unsold puzzles and took them to Tokyo (where he sold them all).  He got my puzzles published in Japan for me, and got me paid for them.  I am just one of many hundreds of puzzlemakers he has helped.

He was one of the founders of the The IPP Puzzle Design Competition. Last year, the grand prize for best new puzzle went to a japanese designer for the third year in a row, which Nob amusingly made mention of while accepting the award on behalf of  Mineyuki Uyematsu.

Nob Yoshigahara
Figure 4. Nob Yoshigahara accepts the Grand Prize for the Puzzle Design of the Year.

Nob developed many Sliding Block puzzles.  Inspired by this, I designed a few myself, using Taniguchi's free sliding block analysis program.

NO-OFF puzzle
Figure 5.  The No-Off Puzzle (java applet).

Put 1-5 on the corners of pentagon. There are 24 ways to do it -- make 12 pentagons, so that the mirror images are on each side of the pentagon.  Thus, 1-2-3-4-5 is on the back of the pentagon with 5-4-3-2-1.  1+2+3+4+5=15. 15 x 12=180. On a dodecahedron, there are 20 apexes. So, 180/20=9 ...... this was Nob's basic design. Put all 12 pentagons on a dodecahedron so that all apexes sum up to nine, with 1+3+5, 1+4+4, 2+3+4, 2+2+5, or 3+3+3. When it was sold in Japan, Nob had only two solutions found manually.  Later, the editor of the Journal of Recreational Mathematics, Harry Nelson, came to Japan. Nob showed him this, and he immediately said "I will find at least ten solutions of this in three months." Nob promptly bet $100 that Harry was mistaken -- that even with a supercomputer, Harry couldn't find ten solutions.  Harry then went back to Lawrence Livermore labs, and started an analysis in his spare time. Eventually, Harry showed Nob all of the solutions on a large printout. Harry won! But Nob obtained 26 minutes of time on a CRAY supercomputer for only $100!

Figure 6.  Nob's Dodeca puzzle. (Task - find all solutions)

Nob developed many puzzles for Hamayana ToysCast Puzzle is the best series of puzzles in the world, highly recommended. 

Figure 7.  The Elk puzzle by Nob.

Another puzzle by Nob: "Pack five of the same pentacubes into a 3 x 3 x 3 box. Because 5 x 5 = 25 and 3 x 3 x 3 = 27, two spaces are left in the box. Among 12 kinds of pentacubes, what shape can be used? P is easy to pack.  U is also possible.  What other pentomino can be used?"

Nob died on 19 June, 2004.  He long had frail health, but he relentlessly promote puzzles right until the end.  In the hours before going into major surgery, for example, he programmed a computer to solve a complex pentomino packing problem.  He didn't want his hours of unconsciousness wasted.  His humor, wit, and force of will made him seem immortal.  I will greatly miss him.

He always signed his letters and challenges the same way, and with that I'll close.

Happy Puzzling Forever! (Nob)


Frédéric Benhamou and Fédéric Goualard, Debugging Constraint Programs by Store Inspection,

Rik van Grol, "2003 Puzzle Design Competition," Cubism For Fun 62, November 2003.

Patrick Hamlyn and Erich Friedman, "Partridge Numbers,"

Hanayama Toys, Cast Puzzles,

George Miller, "TriPenta Hexagon,"

Ivars Peterson, "It's Not You, It's the Puzzle,"

Ivars Peterson, "Five-Suit Decks, Traffic-Jam Puzzles, and Other Treats,"

Ishi Press,

Kate Jones, "Puzzling Pentagon,"

Scott Kim, Rock Collecting (The Hiroimono puzzle),

John Rausch, "Puzzles by Nob Yoshigahara,"

Jaap Scherphuis, "Rubik's Revenge," Jaap's Puzzle Page,

Yoshiya Shindo, "Ultim-Eight,"

Atelier Tamura, "Put-Together Puzzles 2,"

Nob Yoshigahara, "A Die on an Overhead Projector," ICME-9: Abstracts for TSG18,

Nob Yoshigahara, Puzzles 101: A Puzzlemaster's Challenge, A K Peters LTD, 2004.

Math Games archives.

Comments are welcome. Please send comments to Ed Pegg Jr. at

Ed Pegg Jr. is the webmaster for He works at Wolfram Research, Inc. as the administrator of the Mathematica Information Center.