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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

A game is played on a 2D board:

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:

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

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:

So the solution is written as the following:

"1L2R4U7R"

Your goal Starting from this initial board:

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

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:

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

Lazar Ilic(3/7/2023 4:12 PM IDT)
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Fabio Michele Negroni(4/7/2023 1:28 PM IDT)
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*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)
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Hakan Summakoğlu(10/7/2023 11:55 PM IDT)
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*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)
*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)
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