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Ponder This

Welcome to our monthly puzzles.
You are cordially invited to match wits with some of the best minds in IBM Research.

July 2023 - Challenge

<< June August >>

A game is played on a 2D board:


The board is represented here with X’s for blanks and the same number for every square of a given piece X112X X122X 34556 74666

During every turn of the game, one piece is chosen and can be moved one step right, left, up or down, given enough free space in that direction.

The cost of moving a piece is 5-s where s is the size of the piece, so moving a piece composed of four squares costs 1, while moving a piece of one square costs 4.

The goal of the game is to arrange the board according to some goal, with minimum cost.

Note that pieces of the same size and shape are considered identical.

For example, given the following goal for the original board above:


11XX2 14X22 34556 X7666

The sequence of steps reaching the goal from the beginning is:



X112X X122X 34556 74666

11XX2 1XX22 34556 74666

11XX2 14X22 34556 X7666

11XX2 14X22 34556 7X666

11XX2 14X22 34556 X7666

The cost of the first 2 moves is 2, the third one is 3, and the last one is 4, totaling 11.

Given a board, a compact way to describe a solution is to number all the pieces, and then write a string of the form "3U5L" etc. to denote moves (first the number of the shape, and then the direction: U=Up, L=Left, R=Right, D=Down).

For the above board, we can use the following numbering:



X112X X122X 34556 74666

So the solution is written as the following:

"1L2R4U7R"

Your goal Starting from this initial board:


12234 12334 56778 99888 XXXXX

Find a solution with a cost of no more than 100 that reaches the following goal:

77X22 XX321 X3341 59948 X6888

A bonus "*" will be given for finding a solution with a cost of no more than 150 which, using the same initial board, reaches the following goal:

X223X 12338 1X888 4XX56 49977

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: 02/07/2023 @ 15:00 PM EST
Solution: 05/08/2023 @ 12:00 PM EST
List Updated: 24/08/2023 @ 15:00 PM EST

People who answered correctly:

Lazar Ilic(3/7/2023 4:12 PM IDT)
*Nathan Salo(3/7/2023 10:24 PM IDT)
*Martin Thorne(3/7/2023 10:27 PM IDT)
Guillaume Escamocher(3/7/2023 10:55 PM IDT)
*Yan-Wu He(4/7/2023 3:04 AM IDT)
Victor Chang(4/7/2023 6:56 AM IDT)
*Evan Semet(4/7/2023 8:12 AM IDT)
*Alper Halbutogullari(4/7/2023 8:33 AM IDT)
*Sanandan Swaminathan(4/7/2023 10:27 AM IDT)
*Harald Bögeholz(4/7/2023 10:57 AM IDT)
Giorgos Kalogeropoulos(4/7/2023 11:17 AM IDT)
*Phil Proudman(4/7/2023 11:50 AM IDT)
Fabio Michele Negroni(4/7/2023 1:28 PM IDT)
*Lyes Belhoul(4/7/2023 5:46 PM IDT)
*Bertram Felgenhauer(4/7/2023 6:51 PM IDT)
*Luka Mushkudiani(4/7/2023 10:20 PM IDT)
*Bert Dobbelaere(5/7/2023 12:40 AM IDT)
Evan Schor(5/7/2023 9:11 AM IDT)
*Hok Leung Nip(5/7/2023 5:17 PM IDT)
*Quentin Higueret(5/7/2023 5:24 PM IDT)
*Savitha Viswanadh Kandala(5/7/2023 8:28 PM IDT)
*Kandala Viswakanth(5/7/2023 8:44 PM IDT)
*Todd Will(5/7/2023 11:15 PM IDT)
*Daniel Chong Jyh Tar(6/7/2023 5:12 AM IDT)
*Nathan Hopkins(6/7/2023 5:54 AM IDT)
*Vladimir Volevich(6/7/2023 7:24 PM IDT)
*Dominik Reichl(6/7/2023 9:11 PM IDT)
*Tim Walters(6/7/2023 11:07 PM IDT)
*Andrew Gauld(7/7/2023 4:23 AM IDT)
*Nicolas Paris(7/7/2023 5:08 PM IDT)
*James Heayes(7/7/2023 5:15 PM IDT)
Reiner Martin(7/7/2023 9:30 PM IDT)
*Prashant Wankhede(8/7/2023 4:13 AM IDT)
*Daniel Bitin(9/7/2023 11:46 PM IDT)
Gary M. Gerken(10/7/2023 5:48 AM IDT)
Kanit Pongteeraroj(10/7/2023 12:04 PM IDT)
*Julien Vincent Pradier(10/7/2023 4:09 PM IDT)
*Armin Krauss(10/7/2023 8:24 PM IDT)
*Dieter Beckerle(10/7/2023 9:36 PM IDT)
Hakan Summakoğlu(10/7/2023 11:55 PM IDT)
*Li Li(11/7/2023 3:02 AM IDT)
*Stéphane Higueret(11/7/2023 9:45 AM IDT)
Andras Varga(11/7/2023 11:05 AM IDT)
*Dan Mayer(11/7/2023 5:52 PM IDT)
*David F.H. Dunkley(11/7/2023 10:52 PM IDT)
*Michael J. Swart(12/7/2023 5:08 AM IDT)
Lazar Ilic(3/7/2023 4:12 PM IDT)
*Nathan Salo(3/7/2023 10:24 PM IDT)
*Martin Thorne(3/7/2023 10:27 PM IDT)
Guillaume Escamocher(3/7/2023 10:55 PM IDT)
*Yan-Wu He(4/7/2023 3:04 AM IDT)
Victor Chang(4/7/2023 6:56 AM IDT)
*Evan Semet(4/7/2023 8:12 AM IDT)
*Alper Halbutogullari(4/7/2023 8:33 AM IDT)
*Sanandan Swaminathan(4/7/2023 10:27 AM IDT)
*Harald Bögeholz(4/7/2023 10:57 AM IDT)
Giorgos Kalogeropoulos(4/7/2023 11:17 AM IDT)
*Phil Proudman(4/7/2023 11:50 AM IDT)
Fabio Michele Negroni(4/7/2023 1:28 PM IDT)
*Lyes Belhoul(4/7/2023 5:46 PM IDT)
*Bertram Felgenhauer(4/7/2023 6:51 PM IDT)
*Luka Mushkudiani(4/7/2023 10:20 PM IDT)
*Bert Dobbelaere(5/7/2023 12:40 AM IDT)
Evan Schor(5/7/2023 9:11 AM IDT)
*Hok Leung Nip(5/7/2023 5:17 PM IDT)
*Quentin Higueret(5/7/2023 5:24 PM IDT)
*Savitha Viswanadh Kandala(5/7/2023 8:28 PM IDT)
*Kandala Viswakanth(5/7/2023 8:44 PM IDT)
*Todd Will(5/7/2023 11:15 PM IDT)
*Daniel Chong Jyh Tar(6/7/2023 5:12 AM IDT)
*Nathan Hopkins(6/7/2023 5:54 AM IDT)
*Vladimir Volevich(6/7/2023 7:24 PM IDT)
*Dominik Reichl(6/7/2023 9:11 PM IDT)
*Tim Walters(6/7/2023 11:07 PM IDT)
*Andrew Gauld(7/7/2023 4:23 AM IDT)
*Nicolas Paris(7/7/2023 5:08 PM IDT)
*James Heayes(7/7/2023 5:15 PM IDT)
Reiner Martin(7/7/2023 9:30 PM IDT)
*Prashant Wankhede(8/7/2023 4:13 AM IDT)
*Daniel Bitin(9/7/2023 11:46 PM IDT)
Gary M. Gerken(10/7/2023 5:48 AM IDT)
Kanit Pongteeraroj(10/7/2023 12:04 PM IDT)
*Julien Vincent Pradier(10/7/2023 4:09 PM IDT)
*Armin Krauss(10/7/2023 8:24 PM IDT)
*Dieter Beckerle(10/7/2023 9:36 PM IDT)
Hakan Summakoğlu(10/7/2023 11:55 PM IDT)
*Li Li(11/7/2023 3:02 AM IDT)
*Stéphane Higueret(11/7/2023 9:45 AM IDT)
Andras Varga(11/7/2023 11:05 AM IDT)
*Dan Mayer(11/7/2023 5:52 PM IDT)
*David F.H. Dunkley(11/7/2023 10:52 PM IDT)
*Michael J. Swart(12/7/2023 5:08 AM IDT)
*Vaskor Basak(12/7/2023 3:50 PM IDT)
*Asaf Zimmerman(12/7/2023 5:59 PM IDT)
*Soonho You(12/7/2023 6:31 PM IDT)
Ritesh Goenka(14/7/2023 7:39 AM IDT)
Matt Cristina(14/7/2023 8:02 PM IDT)
*Guy Daniel Hadas(15/7/2023 11:43 PM IDT)
*Jim Clare(16/7/2023 2:22 AM IDT)
*Sri Mallikarjun J(16/7/2023 5:16 PM IDT)
*Alain Michiels(16/7/2023 8:11 PM IDT)
*K S(17/7/2023 5:04 AM IDT)
*Nyles Heise(17/7/2023 8:08 AM IDT)
Alex Fleischer(17/7/2023 12:15 PM IDT)
*William Cho(18/7/2023 5:51 AM IDT)
Hansraj Nahata(19/7/2023 4:19 AM IDT)
*Karl Mahlburg(19/7/2023 4:40 AM IDT)
*Paolo Farinelli(19/7/2023 4:24 PM IDT)
Austin Lee(19/7/2023 5:34 PM IDT)
Teawoo Kim(19/7/2023 10:24 PM IDT)
*Diane Pham(20/7/2023 3:40 PM IDT)
*Digant Patel(21/7/2023 4:33 PM IDT)
*David Greer(22/7/2023 2:00 PM IDT)
*Fakih Karademir(22/7/2023 2:03 PM IDT)
Lorenz Reichel(22/7/2023 6:59 PM IDT)
Gail Jardine(22/7/2023 9:33 PM IDT)
*Digant Patel(23/7/2023 10:39 AM IDT)
*Christian Romon(23/7/2023 11:49 AM IDT)
*Nikita Sirons(23/7/2023 12:47 PM IDT)
*Greg Janée(23/7/2023 5:20 PM IDT)
*Hansraj Nahata(23/7/2023 5:26 PM IDT)
Aaron Kim(24/7/2023 2:42 AM IDT)
*Michael Liepelt(24/7/2023 9:44 PM IDT)
*Chris Shannon(25/7/2023 9:57 AM IDT)
Kay Lee(26/7/2023 3:29 PM IDT)
Olivia Jezler & Stefan Wirth(27/7/2023 4:45 AM IDT)
*Petro Mudrievskyj(27/7/2023 8:31 AM IDT)
*Daniel Lincke(27/7/2023 1:10 PM IDT)
Yannick(28/7/2023 12:44 PM IDT)
*Kang Jin Cho(29/7/2023 2:36 AM IDT)
Daniel Copeland & Isaac Lawrence & Raphael Deem(29/7/2023 10:31 AM IDT)
*José Eduardo Gaboardi de Carvalho(30/7/2023 11:12 PM IDT)
*Latchezar Christov(31/7/2023 10:10 PM IDT)
*Marco Bellocchi(1/8/2023 7:13 PM IDT)
*Radu-Alexandru Todor(2/8/2023 2:21 AM IDT)
Diogo Cavaco(2/8/2023 11:57 AM IDT)
*Motty Porat(3/8/2023 12:12 AM IDT)
Mansi Pai(3/8/2023 6:28 PM IDT)
Blaine Hill(3/8/2023 10:16 PM IDT)
Arash Yazdani(4/8/2023 6:58 PM IDT)
Xiao Liu(5/8/2023 11:50 PM IDT)
*Govind Jujare(23/8/2023 11:45 PM IDT)