June 2025 - Challenge
This puzzle was suggested by Gyozo Nagy - thanks!
We play the following game on an N\times N board: We control a frog that starts somewhere on the board. The cells of the board can be either white ("empty"), blue ("visited"), or red ("forbidden"). At the beginning of the game, the whole board is white except for a blue cell where the frog starts. On each step of the game, the frog moves to one of the eight adjacent cells. We denote the possible moves with the letters A, B,...,H clockwise around the current cell, such that A is a move to the cell directly to the right, B is a move to the cell below and to the right, and so on around the current location of the frog. To move to a cell, the following conditions must apply:
After the move is performed, the cell now containing the frog turns from white to blue.
In addition, the next cell in the same direction (the one that could not be blue), if it exists, becomes red (or remains red if it was already that color).
The goal of the game is to reach a state where only non-white cells remain on the board (the number of red or blue cells does not matter).
For example, in a 4x4 board starting from (0,0) (the top-left corner), performing the sequence of moves "ABHCDBEFDGH" results in a fully colored board with 4 red cells.
Your goal: Solve the game for a 20x20 board starting from (0,0). Give your solution as a string of letters as shown above.
A bonus "*" will be given for solving the game for a 10x10 board starting from (4,4).
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:
29/05/2025 @ 15:00 PM EST
Solution:
05/07/2025 @ 12:00 AM EST
List Updated:
16/06/2025 @ 14:05 PM EST
*Bertram Felgenhauer(29/5/2025 5:45 PM IDT)
*Lazar Ilic(29/5/2025 8:07 PM IDT)
*John Tromp(30/5/2025 12:58 AM IDT)
King Pig(30/5/2025 3:44 AM IDT)
*Sanandan Swaminathan(30/5/2025 12:09 PM IDT)
*Alper Halbutogullari(30/5/2025 3:02 PM IDT)
*Jordan Payette(30/5/2025 3:52 PM IDT)
*Bert Dobbelaere(30/5/2025 4:04 PM IDT)
*Shirish Chinchalkar(30/5/2025 10:29 PM IDT)
*Ankit Aggarwal(31/5/2025 1:43 AM IDT)
*Griffin Pinney(31/5/2025 5:07 AM IDT)
*Stephen Ebert(31/5/2025 5:50 AM IDT)
*Loukas Sidiropoulos(31/5/2025 6:17 PM IDT)
*Gary M. Gerken(31/5/2025 6:26 PM IDT)
*Resnina (Kulshaeva) Tathyana(31/5/2025 8:21 PM IDT)
*Motty Porat(31/5/2025 8:36 PM IDT)
*Gyozo Nagy(1/6/2025 12:03 AM IDT)
*Sri Mallikarjun J(1/6/2025 9:45 AM IDT)
*Yi Jiang(1/6/2025 11:42 AM IDT)
*Harald Bögeholz(1/6/2025 2:14 PM IDT)
*Juergen Koehl(1/6/2025 8:01 PM IDT)
*Klaus Nagel(1/6/2025 10:29 PM IDT)
*Latchezar Christov(1/6/2025 11:53 PM IDT)
*Lorenz Reichel(2/6/2025 2:26 PM IDT)
*Jiri Spitalsky(2/6/2025 4:12 PM IDT)
*Paul Revenant(3/6/2025 12:59 AM IDT)
*Daniel Bitin(3/6/2025 3:59 PM IDT)
*Martin Thorne(3/6/2025 7:10 PM IDT)
*Fakih Karademir(4/6/2025 10:14 PM IDT)
*Kevin Bauer(5/6/2025 12:37 AM IDT)
Dan Ismailescu(5/6/2025 10:37 PM IDT)
*Dominik Reichl(6/6/2025 12:52 PM IDT)
*Nadir S.(6/6/2025 10:24 PM IDT)
*Hakan Summakoğlu(7/6/2025 5:54 PM IDT)
*Erik Hostens(8/6/2025 9:42 AM IDT)
*Sean Kuwamoto(8/6/2025 9:47 AM IDT)
*Camden Chappelle(9/6/2025 3:57 AM IDT)
*Marcel Caria(9/6/2025 2:00 PM IDT)
Mithil Ramteke(9/6/2025 7:15 PM IDT)
*Mark Mammel(10/6/2025 3:14 AM IDT)
Fabio Michele Negroni(10/6/2025 5:09 PM IDT)
*Yash Kumar Kasaudhan(12/6/2025 9:21 AM IDT)
Ansh Kasaudhan(12/6/2025 9:26 AM IDT)
*Kang Jin Cho(12/6/2025 10:58 AM IDT)
*Paul Lupascu(13/6/2025 7:41 AM IDT)
*Franciraldo Cavalcante(14/6/2025 2:21 AM IDT)
*Peter Moser(14/6/2025 11:19 AM IDT)
*David F.H. Dunkley(15/6/2025 2:20 AM IDT)