Ponder This Challenge - July 2016 - Pentominos tiling (Golomb)

Ponder This Challenge:

This month's challenge is in honor of the late Professor Solomon Golomb (https://en.wikipedia.org/wiki/Solomon\_W.\_Golomb), who received the National Medal of Science from President Obama on February 2, 2013. Prof. Golomb received his award in the same ceremony as Rangaswamy Srinivasan from IBM, who was awarded his medal for contributions to laser eye surgery.

Golomb proved that any 2^Nx2^N board with a missing square can be tiled with a single r-shaped tromino.

Find at most three types of pentominos (http://mathworld.wolfram.com/Pentomino.html) that can tile every 4^Nx4^N board with a missing square.

Prove your solution.

Solution

• Click here to view the solution

  A high school student (Arthur Befumo) and an IBMer (Jonathan Lenchner) wrote a paper "Extensions of Golomb's Tromino Theorem" (https://fwcg14.cse.uconn.edu/program/wp-content/uploads/sites/863/2014/10/fwcg2014_submission_10.pdf) that solves this month's problem.

  Many of you solved with P and Y or P and L. See Jesse Rearick's drawing here on how to solve it with P and L pentominos.

Solvers

• *Robert Gerbicz (30/06/2016 07:57 PM IDT)
• *Stefano Leucci (30/06/2016 07:50 PM IDT)
• Bert Dobbelaere (30/06/2016 09:03 PM IDT)
• *Lorenz Reichel (30/06/2016 09:31 PM IDT)
• *Radu-Alexandru Todor (01/07/2016 02:53 AM IDT)
• *Jesse Rearick (01/07/2016 06:50 AM IDT)
• *Jimmy Waters (01/07/2016 07:08 AM IDT)
• *Kang Jin Cho (01/07/2016 07:29 AM IDT)
• *Joseph DeVincentis (01/07/2016 03:56 PM IDT)
• *Siddharth Joshi (01/07/2016 05:09 PM IDT)
• *Motty Porat (01/07/2016 05:47 PM IDT)
• *Florian Fischer (01/07/2016 05:56 PM IDT)
• Zhuo Wang (01/07/2016 07:36 PM IDT)
• Sergey Koposov (01/07/2016 09:37 PM IDT)
• *Amir Sarid (02/07/2016 01:23 AM IDT)
• *Harald Bögeholz (02/07/2016 10:52 AM IDT)
• *Hendrik Nigul (02/07/2016 12:30 PM IDT)
• *Mathias Schenker (02/07/2016 12:31 PM IDT)
• *Benjamin Lui (02/07/2016 04:29 PM IDT)
• *Hanlin Ren (02/07/2016 05:57 PM IDT)
• *Mtv Europe (03/07/2016 06:01 PM IDT)
• Alex Fleischer (03/07/2016 10:55 PM IDT)
• *David Greer (04/07/2016 01:38 AM IDT)
• *Serge Batalov (04/07/2016 04:00 AM IDT)
• *Yuan Li & Ye Fan (04/07/2016 12:56 PM IDT)
• *Frank Schoeps (04/07/2016 04:23 PM IDT)
• *Roberto Tauraso (04/07/2016 06:27 PM IDT)
• *David F.H. Dunkley (04/07/2016 10:45 PM IDT)
• *Luke Pebody (04/07/2016 11:39 PM IDT)
• *David Friedman (05/07/2016 06:53 AM IDT)
• *Paolo Farinelli (05/07/2016 06:08 PM IDT)
• *Thomas Rohr (05/07/2016 07:38 PM IDT)
• *Alexander Shay Geller​ (05/07/2016 09:38 PM IDT)
• *Shen Huang (06/07/2016 07:31 AM IDT)
• *Matthew Charlap (06/07/2016 04:03 PM IDT)
• *Tamir Ganor & Shouky Dan (06/07/2016 06:04 PM IDT)
• *Phil Muhm (06/07/2016 06:55 PM IDT)
• *Andreas Stiller (06/07/2016 07:34 PM IDT)
• *Gerhard Hoffmann (& Klaus Hoffmann) (06/07/2016 10:42 PM IDT)
• *Liubing Yu (07/07/2016 12:28 AM IDT)
• *Daniel Chong Jyh Tar (07/07/2016 07:05 PM IDT)
• *Jens Voss (07/07/2016 07:20 PM IDT)
• *Pål Hermunn Johansen (08/07/2016 01:28 AM IDT)
• *Franciraldo Cavalcante (08/07/2016 06:05 AM IDT)
• *Clive Tong (09/07/2016 03:59 PM IDT)
• *M Zecevic (11/07/2016 02:50 AM IDT)
• *Davor Obradovic (11/07/2016 05:01 AM IDT)
• *Roman Lee (11/07/2016 08:24 AM IDT)
• *Chuck Carroll (11/07/2016 02:24 PM IDT)
• *Asaf Rosin (11/07/2016 10:40 PM IDT)
• *Lavanya Kannan (11/07/2016 11:53 PM IDT)
• *Tom Sirgedas (11/07/2016 11:59 PM IDT)
• *Erik Hostens (12/07/2016 04:46 PM IDT)
• *Hugues Juillé (12/07/2016 05:16 PM IDT)
• *Muralidhar Seshadri (12/07/2016 05:33 PM IDT)
• *Jim Clare (13/07/2016 01:25 AM IDT)
• *Ante Turudic (13/07/2016 10:31 AM IDT)
• *Andreas Eisele (15/07/2016 10:43 AM IDT)
• *Shirish Chinchalkar (15/07/2016 03:21 PM IDT)
• *Hao Zheng 15/07/2016 (11:43 PM IDT)
• *Masky Ng (19/07/2016 11:47 AM IDT)
• *Ranjit Eswaran (19/07/2016 02:29 PM IDT)
• *Stijn Vermeeren (19/07/2016 03:42 PM IDT)
• *Hooman Habibi (19/07/2016 04:54 PM IDT)
• *Emir Haleva (24/07/2016 10:34 PM IDT)
• *Raymond Lo (24/07/2016 10:50 PM IDT)
• *Michael D Schuresko (25/07/2016 12:28 AM IDT)
• *Ferenc Wettl (25/07/2016 06:25 PM IDT)
• *Hyunsun Kim (25/07/2016 09:00 PM IDT)
• *Sri Mallikarjun J (26/07/2016 07:44 AM IDT)
• *T.K. Chang (26/07/2016 07:32 PM IDT)
• *Albert Stadler (26/07/2016 11:41 PM IDT)
• *Mat Newman (27/07/2016 02:29 PM IDT)
• *Yue Ru Sun (28/07/2016 08:59 AM IDT)
• *Antons Šušpans (28/07/2016 11:12 PM IDT)
• *Jackie ByeongYeon Ryu (30/07/2016 04:56 PM IDT)
• *Vibhakar Shukla & Vivek Chaurasiya (31/07/2016 03:10 AM IDT)
• *Erik Wünstel (31/07/2016 11:15 PM IDT)
• *Wilder Boyden (01/08/2016 02:06 AM IDT)
• *Jang Hun Choi (01/08/2016 06:12 AM IDT)