Puzzle
12 minute read

Ponder This Challenge - April 2025 - Klumpengeist

In the game of Klumpengeist, the player controls a giant cube (the "Klumpengeist"), which can devour inanimate objects and grow larger as a result. The larger the cube becomes, the larger the objects it can devour. Its goal: either eat all the objects in its vicinity as quickly as possible or grow as large as possible within a specific amount of time.

The size of the cube is determined by its growth points (GP). The initial value of GP is 1, and the size of the cube is the largest nn such that n2n^2 is less than or equal to its GP. For GP 1, the size is 1; for GP 13, the size is 3; for GP 25, the size is 5, and so on.

We represent the game board as an array of numbers, e.g.,

0 1 1 2
1 3 0 1
2 0 0 4
0 2 1 3

The player begins in the top-left corner. The numbers on the board represent the sizes of the objects in each cell; 0 denotes an empty cell. To enter a cell, the Klumpengeist must be of a size greater than or equal to the size of the object in that cell. In this case, it devours the object, the cell becomes empty, and that object's size is added to the Klumpengeist's GP.

In the example above, the Klumpengeist can go RIGHT or DOWN at the beginning, but going DOWN will result in it having GP 2, which is not enough to continue moving DOWN again. However, if it returns UP to the first row and moves RIGHT and then RIGHT again, it will reach GP 4. This means it will reach a size of 2 and be able to devour the 2 in the upper-right corner.

An example of a path for the Klumpengeist that devours all the objects on the board is:

RRDRULLLDDURDDRRU

This path contains 17 steps.

Your goal: Find a path with at most 500 steps that devours all the objects on the board

 0  0  1  5  1  0  0  0  0  0  1 19  0  7  4  2  7 12  7  1
 2  6  0  0  1  8  0  8  1  2  1  0  8  9  1  7 10 13 10  6
 4 11  6  7  5  5 14  1 12  1  0  2  0  2  2  5  1 10  0 14
15 12  2  5 18  6 19 16 18 11 14  3  1  2  3  3  8  2  1  9
 5  6  8 18  4 17  7 16 14 13  4 13  8  1  2  2  7  5 11 12
 6  7 13 16  1 14  7 17 18  9 14  6 16 10  0  3  2  0  6  5
11  5 11  3 14 19 19  4 17 16  3 12 17 17  1  2 12  6  7 11
18  6  6  3 19 13  7  9  5 13  4  4  2 13  2  0  0  5  4  6
17 19  7  2  4  3  4  1 16  9 13 17 17 15  6  9  1  5  2  0
 8  8 17 18 10 12 10  0  0 13 13 10  8  0  0  7 18 10  6  3
13  3 19  3  5  9 17 16 12  2 19  9  1 17  3  0 10 11  4 19
14  5 11 13 15  6  5 10  6  1  7  3  4 15 10 10 13  4  9  7
 2 12  5  7  7 16  3  2 18 14 11 18 12 15  4  2 12 15 10  6
12  5  2 15  8  9 18  9  5  1 17 17  1  0  8  9  5  6  8 13
 9 13  5  3  9  8 18 15 10  6 12 18 11 15  2 12  6  8 12 15
14  4  2  0 13  2 18 12 16  2  4 13  0  3 16 15 15 16  7  7
 6 12  1 14  4 12  8 14 10  0 15 16 13  4  5 12  5  2 16 12
 5  5  3  0  8  0  5 16 11  4 17 13 18 17  0  9  8 16 13  6
15 13 13  5  6  7  9 15 12 18  2 12 19  4  9  5  6  8  9  3
12 10 11  2  5  8 11  7 16 12  0 14 10  5  9  0 15  4 11  3

Provide your result as a string of "U", "D", "R", and "L", as shown in the example above.

A bonus "*" will be awarded for finding a path of at most 150 steps that reaches a size of 30 on the following board:

 0  1  0  0  0  5 16  8 15  4  5  5 17 17  7 11 18  4 16 15  9 17  1  3 19  6  4 16  3  7
 6  3 13 11  1  5 10 18  8 18  8  8  3 10 18  4  2  8  3  1 11 12 11 15 12  8 14  5  4  9
 9  0 15  4  1 11  1 11 17  8  4  6  4 12 16 19  9  8  4  2 18 12  1  4  4 10 10  4  9  2
10 10  2  9  1 19 19 16 19 18  2  4 17  6  8  1 14  9 13  4  1  4 10  2 11  2  7  8 10 15
11  6 14  1  0  8  4  9  3 16  6  6 14  9  5 19 13  5  5  0 17 18  8 17  6  4  5 17  5 15
 0  1  0  0  7  1  8  0  4  3  3  5 10 16  2  9 18 17 17  6 14 15 13 12  1  8 15  1  9  1
 0  1  1  0 19  4  1  0 13  4  4  6  3 11 11  1 19 17 12  7 16 17  0 18  0 14 17 18 17 18
16 14  5  1  3  0 18 12 15  7  2  0  2  2  8 13  3  9 13 13 18  3  1 12 18 19  1  6 16  0
 7 13 15  9  0  1  4 15  8  3 19 12  4  0  2  1 11 19  6  3  0 14  5 15  7  4  3 15 10 15
19 16 11  8  3  2 10 13 10 14 11 12 10 18  6  2  7  9 11 10  4 14 10  6 11  4 12  5 17 10
 9  0 10 19 19 11 14 19 17  3  4  8 11  4  3  6  8 12  4  8  4  3 16 10  4 10 12 10 19  0
18 17  1 17 19  5  3 10 10 19 17  6  6 14  3  2  8  5  1  2  8 10  7  4 18 10  5  3  9  6
10 16  0 17 11 10 14  1 11  1  2 14 16  4  8  2 10  2  8  8 18 12 18 13 18  1 17 18  8  2
 2 11  8 11 12 15  0  5  8  3  4  6  6  7  6 15  7  7 13 18 13 12 14  9 15  0 15  8  1  7
 2  6 17 14  5 14  0  8  1 11 13 13 19 13  5  1  8  9 18  5  1 16 14 11  9  2 12 18 10 19
15  2 15 17  8  5 11 18 16 10  7  1 17 18 19  9  4 13 12  6  3  2  4  5  0 13 13 17 19 12
17  4  4 17  8 14  6 12 18 14 13  7 17  5 19 18  9 11 11 10  6 17 19  6 13 19  7  0 14  5
 8  9 10  2 19  3  7 10  9 14 16  3  6  4  1 15 13  8  5  0 14  8  6  0  1  3 14  1 13 10
12  3 10 18  5 19 17 16  5 12 14 19  6 13 15  3  1 15 15  4 10  9 12  2 19  3 10 13 12  2
19 18 17 19  2 18 16  5  6  4 12 10  0  1  5 12 10 18  3  0  3 12 14  2 16 13  9 15 10 15
17  5 19 16 14  6  2 15  9 14 19 15  7 15 16  6 12  1  8 12  2 14 12 18  4  4  4 12 12 17
 6 12  7 17  0 11 17 11  5 12 13  6  4 13 15 16  9 16 15  3 13 11  3 17 14  9  5  5  5 12
 3  0  4 15 16  4 17  2  2 16  0  1  7  4  3  0  4  2  9 13 13  4 15 10 16  0  1  5  1  2
 6  1  9  6  9  9  8 18  2  5  2  9 19  0 12  7  0 17  4  3 19 10 12 14 10  8  6  6 10 19
 6 11 13  2 17 11  3  1 18 13 12  0 11  7  2 12  9  3 13  8  2  1 17 19 11 19  5  0  2 15
13 19 12 17  9 18 13  9  1 12  6  9 15 13  9  3  4  4  0 15 15  4 16  9 16 13  1 13  4  6
17  5 11  3  3 15  9 16  8  1 15 14  9 12 13  8 17  1 16  7 15 17 18  8 11 16 19 14  7  8
 6 10 18 16  4 10  2 14  6  2  1  1 18  0  6 17  6 15 17  0  5 13 11  4  8 10  8  1 10 13
13  0  3  2  9 14  3  5 14 11  4 13  0  8  5 14 14  8 19  7 14 10 16 14  8 19 19  2  6 19
 5  3  4  5 10 19  2  5  8 10  9  6 11  4  4 12 10 15 17 15  8  9  5 19 14 16 12 16 16  5

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

Solution

  • April 2025 Solution:

    The best solutions received were the following length 397 solution by Radu-Alexandru Todor

    RRDRRURRRRDRDRRDRRURDRUDDLDDDRUURRRDLDRDLLLLDRDLDRDLDRDRUUUURDRDLDRDLDRDLLULDLUULDDLLLURRULLUURDRURUULDLULDLU
URURDRURUUUULLDRDDLULDLDLUURURUULDLDLUURULULLDRDLDRDLLUUULUUDDDDDLUUULULDDRDLDRDLDRRURDRURDRURDDLLLLLLLDRRRRR
RDRRDLLLULDLULDLULDDDDDDDDDRUUUUUUURDDDDDDDRUUUUUUURDDDDDDDRUUUUUUURDDDDDDDRUUUUUUURRDLDRDLDDRDLDRRUURDDRUURD
DRURURDDRUURDDRUUUUUUUUULULLRRRUUUUULLLDDUUUURDRRUUULDLULDLULDLULDLULD

    and length 401 solution by Dominik Reichl

    RRDRRURRRRDRRRDDRRRDRDDLDRRDRRULUULURULLULLLURURDRURDDRRURULLDDRRDLDRDLDRDDDLLUULULDDDRDRRRDDDDDDDDDLLLURRUUU
UUUULDDDDDDLLDLDLUUURRRULLLURRRULLURRULLULDDLDDLDDRDDDLUULDLDLLLLLLLLLURRRRRRRRURRUUUURUURUUURRLUUUULLDRDLDRL
DDDLDDLDDDLDLDLULLDLLLLURRRULLLUUUUUUUUUUUUUURDDDDDDDDDDDDDRUUUUUUUUUUUUUURDDDDDDDDDDDDDDDRRRRURUUURULLDDDLDL
LURURULLDUUUUUUUUUUURDDDDDDDDDRUUUUUUUUURDDDDDDDRRDRUULLURRULLURRULLURUURR

    who also found the bonus solution

    RRRRDDDDLDLLDRRDRDDRUUURRURRDRUUUURDDDDRDRRDDRRDDDDDDDRRULUURUUUUUURURUURRRDDDRRURRRDDDDDDLLDDRDRDDDLDDRRDDDD
LDL

    In general, the Klumpengeist problem can be viewed as a variant of the travelling salesperson problem, hence NP-complete and thus should be solved using heuristics and smart search algorithms; but the bound on the number of steps was set very high (maybe too high) leading some of you to code the game themselves (maybe with a little help from AI) and solving it manually by playing. If you like this game, you might want to check out Katamari Damacy.

Solvers

  • *Bertram Felgenhauer (30/3/2025 5:15 PM IDT)
  • *Paul Revenant (30/3/2025 5:36 PM IDT)
  • *Lorenz Reichel (30/3/2025 7:07 PM IDT)
  • *Lazar Ilic (30/3/2025 7:21 PM IDT)
  • *Robert Hannah (30/3/2025 9:10 PM IDT)
  • *Dan Dima (30/3/2025 11:38 PM IDT)
  • *Ankit Aggarwal (31/3/2025 12:44 AM IDT)
  • *Gary M. Gerken (31/3/2025 1:10 AM IDT)
  • *Matt Rearick (31/3/2025 5:39 AM IDT)
  • *Stephen Ebert (31/3/2025 10:17 AM IDT)
  • *Sanandan Swaminathan (31/3/2025 1:30 PM IDT)
  • Ruben Menendez (31/3/2025 2:20 PM IDT)
  • Florian Sikדora (31/3/2025 4:14 PM IDT)
  • *Latchezar Christov (31/3/2025 5:59 PM IDT)
  • *Daniel Chong Jyh Tar (31/3/2025 8:06 PM IDT)
  • *King Pig (31/3/2025 8:20 PM IDT)
  • *Alper Halbutogullari (1/4/2025 5:21 AM IDT)
  • *Paul Lupascu (1/4/2025 11:08 AM IDT)
  • *Loukas Sidiropoulos (1/4/2025 2:26 PM IDT)
  • *Dominik Reichl (1/4/2025 9:17 PM IDT)
  • *Robin Guilliou (1/4/2025 10:14 PM IDT)
  • Gyozo Nagy (2/4/2025 1:07 AM IDT)
  • *Kennedy (2/4/2025 2:06 AM IDT)
  • *Reiner Martin (2/4/2025 4:49 PM IDT)
  • Fabio Michele Negroni (2/4/2025 6:38 PM IDT)
  • *Bert Dobbelaere (2/4/2025 8:22 PM IDT)
  • *Vladimir Volevich (2/4/2025 9:07 PM IDT)
  • *Juergen Koehl (2/4/2025 9:41 PM IDT)
  • *Giovanni Basso (2/4/2025 9:54 PM IDT)
  • Nadir S. (3/4/2025 12:11 AM IDT)
  • *Ankit Chakraborty (3/4/2025 2:16 AM IDT)
  • *Kieran Mackle (3/4/2025 8:32 AM IDT)
  • Shirish Chinchalkar (3/4/2025 9:24 AM IDT)
  • *Nick Trapp (3/4/2025 9:39 AM IDT)
  • *Joydeep Paul (3/4/2025 4:48 PM IDT)
  • *Stéphane Higueret (3/4/2025 6:41 PM IDT)
  • *Harald Bögeholz (4/4/2025 12:03 AM IDT)
  • *Jiri Spitalsky (4/4/2025 8:54 PM IDT)
  • *Balakrishnan V (5/4/2025 5:51 AM IDT)
  • Rethna Pulikkoonattu (5/4/2025 8:18 AM IDT)
  • *Tom Hood (5/4/2025 9:08 AM IDT)
  • *Ward Beullens (5/4/2025 2:07 PM IDT)
  • *Hakan Summakoğlu (6/4/2025 12:58 AM IDT)
  • *Resnina (Kulshaeva) Tathyana (6/4/2025 1:51 AM IDT)
  • *Yi Jiang (6/4/2025 7:12 AM IDT)
  • *Hugo Pfoertner (6/4/2025 7:52 PM IDT)
  • Nathaphon Surarit (6/4/2025 8:01 PM IDT)
  • *Daniel Bitin (7/4/2025 12:10 AM IDT)
  • *Steffen Wolf (7/4/2025 7:39 PM IDT)
  • *Dieter Beckerle (7/4/2025 10:58 PM IDT)
  • *Peter Huggins (7/4/2025 11:36 PM IDT)
  • *Stefan Wirth (8/4/2025 4:00 AM IDT)
  • Zach Liu (8/4/2025 4:01 AM IDT)
  • *Rob Pratt (8/4/2025 8:05 AM IDT)
  • *Rajesh Sathiyanarayanan (8/4/2025 4:26 PM IDT)
  • *Martin Thorne (8/4/2025 7:43 PM IDT)
  • *Christoph Baumgarten (8/4/2025 9:57 PM IDT)
  • Luca Cavallini (8/4/2025 11:57 PM IDT)
  • *Mathias Schenker (9/4/2025 12:31 PM IDT)
  • *Piyush Agrawal (9/4/2025 3:18 PM IDT)
  • *Mark Mammel (10/4/2025 3:58 AM IDT)
  • *Kang Jin Cho (11/4/2025 7:47 PM IDT)
  • *Nischal Agrawal (12/4/2025 3:56 PM IDT)
  • Tamir Ganor & Shouky Dan (12/4/2025 5:21 PM IDT)
  • *Reda Kebbaj (13/4/2025 1:47 AM IDT)
  • *Karl Mahlburg (15/4/2025 4:13 AM IDT)
  • *Jordan Payette (16/4/2025 6:02 PM IDT)
  • *Amos Guler (17/4/2025 9:05 PM IDT)
  • *Kevin Bauer (19/4/2025 2:29 AM IDT)
  • *David Greer (19/4/2025 12:58 PM IDT)
  • *Sri Mallikarjun J (20/4/2025 5:16 PM IDT)
  • *Franciraldo Cavalcante (20/4/2025 9:38 PM IDT)
  • John Ritson (21/4/2025 1:24 AM IDT)
  • *Nyles Heise (21/4/2025 6:37 AM IDT)
  • Michael Vahle (21/4/2025 8:22 PM IDT)
  • *Serge Batalov (21/4/2025 10:11 PM IDT)
  • Radu-Alexandru Todor (21/4/2025 10:46 PM IDT)
  • *Soonho You (22/4/2025 3:00 PM IDT)
  • *Griffin Pinney (23/4/2025 7:33 AM IDT)
  • *Alexandre St-Laurent (24/4/2025 12:40 AM IDT)
  • Michael Liepelt (24/4/2025 12:12 PM IDT)
  • *Fakih Karademir (25/4/2025 12:51 AM IDT)
  • *Frank Schoeps (26/4/2025 2:27 PM IDT)
  • Marshall Munsch-Hayhurst (26/4/2025 7:20 PM IDT)
  • *Klaus Nagel (26/4/2025 7:39 PM IDT)
  • *Marco Bellocchi (26/4/2025 10:22 PM IDT)
  • *Chris Shannon (28/4/2025 6:45 AM IDT)
  • *Evan Semet (29/4/2025 4:01 AM IDT)
  • Mohit Garg (29/4/2025 8:21 AM IDT)
  • *Motty Porat (30/4/2025 7:39 PM IDT)
  • *John Tromp (30/4/2025 10:16 PM IDT)
  • *David F.H. Dunkley (1/5/2025 3:45 AM IDT)
  • *Avi (3/5/2025 11:57 PM IDT)
  • *Camden Chappelle (4/5/2025 1:07 AM IDT)
  • *Li Li (4/5/2025 8:57 AM IDT)
  • *Sherman Yuen (4/5/2025 2:13 PM IDT)

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