July 2024 - Challenge
This riddle was suggested by Evert van Dijken - thanks, Evert!
Consider square tiles made of 4\times 4 squares that can be either black (0) or white (1), such that each tile has an equal number of black and white squares.
We call two tiles equivalent if one can be rotated and/or reflected in order to obtain the other. It is easy to see that a tile can have 1, 2, 4 or 8 equivalent tiles (including itself).
Your goal: Find a tiling of a 16\times 16 squares board (4 x 4 of such tiles, with 4 x 4 squares in each tile) such that:
- 1. In each row and column, there are no more than two consecutive squares of the same color.
- 2. The total number of pairs of adjacent same color squares is minimal. Remember to count both vertical and horizontal pairs.
- 3. All tiles included in the tiling must be non-equivalent
- 4. As stated earlier, each tile must have the same number of black and white squares.
113 1101001010101001 1010110101010110 0101001010101001 0010110101010110 1101001010101101 0010110101010010 0101100110110100 1010011001001011 0101100100110100 1001001010010010 0010010101101101 1101101101101011 0010010010010010 0011001100110100 1100110101001011 1011011011011011
A bonus "*" will be given for solving the above problem, but for a 20\times 20 squares board with the additional constraint that one can only use tiles which have exactly 4 equivalent ones as defined above.
We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!
We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.
If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com
Challenge:
30/06/2024 @ 16:00 PM EST
Solution:
05/08/2024 @ 12:00 AM EST
List Updated:
25/07/2024 @ 10:20 AM EST
Lazar Ilic(2/7/2024 12:52 PM IDT)
Michał Franczak(2/7/2024 9:31 PM IDT)
Alex Fleischer(2/7/2024 10:33 PM IDT)
King Pig(3/7/2024 1:06 AM IDT)
*Yi Jiang(3/7/2024 3:01 AM IDT)
*Bert Dobbelaere(3/7/2024 6:12 AM IDT)
*Bertram Felgenhauer(3/7/2024 12:40 PM IDT)
Yury Volvovskiy(3/7/2024 4:44 PM IDT)
Jiri Spitalsky(4/7/2024 12:00 PM IDT)
Loukas Sidiropoulos(4/7/2024 4:51 PM IDT)
Joaquim Carrapa(5/7/2024 1:12 AM IDT)
Gary M. Gerken(5/7/2024 5:07 AM IDT)
*Yan-Wu He(5/7/2024 8:13 PM IDT)
*Jared Kittleson(5/7/2024 8:14 PM IDT)
*Vladimir Volevich(6/7/2024 1:22 AM IDT)
*John Spurgeon(6/7/2024 9:22 PM IDT)
*Sanandan Swaminathan(8/7/2024 8:36 AM IDT)
*Daniel Chong Jyh Tar(8/7/2024 10:22 AM IDT)
Alper Halbutogullari(8/7/2024 2:59 PM IDT)
Guglielmo Sanchini(8/7/2024 7:17 PM IDT)
*Daniel Bitin(9/7/2024 1:40 AM IDT)
Lorenz Reichel(9/7/2024 8:16 PM IDT)
*Lawrence Au(11/7/2024 6:56 PM IDT)
Kipp Johnson(12/7/2024 4:47 PM IDT)
Alain Michiels(12/7/2024 6:26 PM IDT)
*Mark Pervovskiy(13/7/2024 1:43 AM IDT)
Evert van Dijken(13/7/2024 8:35 AM IDT)
Hakan Summakoğlu(14/7/2024 1:20 AM IDT)
*Ido Meisner(14/7/2024 11:34 PM IDT)
Hugo Pfoertner(16/7/2024 6:14 PM IDT)
Adrian Neacsu(17/7/2024 12:09 AM IDT)
*Nyles Heise(17/7/2024 7:13 AM IDT)
*Latchezar Christov(17/7/2024 4:31 PM IDT)
*Todd Will(17/7/2024 5:22 PM IDT)
*David F.H. Dunkley(18/7/2024 3:35 PM IDT)
*Dieter Beckerle(18/7/2024 6:58 PM IDT)
Julian Ma(19/7/2024 6:32 PM IDT)
*David Greer(20/7/2024 6:29 PM IDT)
*Franciraldo Cavalcante(23/7/2024 12:18 AM IDT)
*Martin Thorne(23/7/2024 7:37 AM IDT)
Guillaume Escamocher(23/7/2024 2:59 PM IDT)
Andreas Stiller(24/7/2024 6:34 PM IDT)
Harald Bögeholz(24/7/2024 9:14 PM IDT)
Tim Walters(24/7/2024 10:54 PM IDT)