October 2024 - Challenge
This puzzle was suggested by Karl Heinz Hofmann - thanks!
We are looking for a natural number X satisfying the following properties of its decimal representation:
1. All the digits \{1,2,3,4,6,7,8,9\} appear at least once, but \{0, 5\} do not appear at all.
2. X can be written as a front part A and back part B, such that if X were a string, it could be written as A concatenated with B, such that
- B is the product of the digits of X.
- X is a multiple of B.
- B is a perfect square.
For example, X=3411296 has the property that its digit product is 1296 so it can be split into A=341 and B=1296 such that properties 2.1 and 2.3 are satisfied. However, none of the other properties are satisfied in this case since X is missing the digits 7,8 and is not a multiple of B.
Your goal: Find the least number X satisfying the above properties.
A bonus "*" will be given for finding the least number X satisfying the above properties except property 2.3 which is replaced by a new property: 2.3 The digit product of A is a perfect cube.
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:
30/09/2024 @ 15:10 PM EST
Solution:
05/11/2024 @ 12:00 AM EST
List Updated:
04/11/2024 @ 10:50 AM EST
*Bertram Felgenhauer(30/9/2024 4:40 PM IDT)
*Lazar Ilic(30/9/2024 5:38 PM IDT)
Paul Revenant(30/9/2024 6:07 PM IDT)
*King Pig(30/9/2024 10:47 PM IDT)
*Andreas Stiller(1/10/2024 3:21 AM IDT)
Alex Fleischer(1/10/2024 8:47 AM IDT)
Yi Jiang(1/10/2024 3:23 PM IDT)
*Griffin Pinney(1/10/2024 4:09 PM IDT)
*Guglielmo Sanchini(1/10/2024 5:17 PM IDT)
John Tromp(1/10/2024 5:47 PM IDT)
*Yan-Wu He(2/10/2024 4:36 AM IDT)
*Robin Guilliou(2/10/2024 2:24 PM IDT)
*Latchezar Christov(2/10/2024 3:07 PM IDT)
*Daniel Bitin(2/10/2024 5:32 PM IDT)
*Lawrence Au(2/10/2024 8:01 PM IDT)
*Hugo Pfoertner(2/10/2024 8:31 PM IDT)
Loukas Sidiropoulos(3/10/2024 3:02 AM IDT)
*Sanandan Swaminathan(3/10/2024 2:10 PM IDT)
*Daniel Chong Jyh Tar(3/10/2024 5:41 PM IDT)
Reiner Martin(3/10/2024 10:52 PM IDT)
*Maksym Voznyy(3/10/2024 11:21 PM IDT)
*Lorenz Reichel(4/10/2024 5:44 PM IDT)
Axel Amestoy(5/10/2024 3:48 PM IDT)
*Harald Bögeholz(5/10/2024 7:38 PM IDT)
William Han(5/10/2024 7:53 PM IDT)
Rudy Cortembert(6/10/2024 11:29 AM IDT)
*Alex Izvalov(6/10/2024 5:39 PM IDT)
Guillaume Escamocher(6/10/2024 6:18 PM IDT)
Sri Mallikarjun J(7/10/2024 5:26 AM IDT)
*Juergen Koehl(7/10/2024 9:24 AM IDT)
*Arthur Vause(7/10/2024 2:09 PM IDT)
*Paul Lupascu(7/10/2024 4:20 PM IDT)
Amos Guler(7/10/2024 6:34 PM IDT)
*Radu-Alexandru Todor(8/10/2024 1:55 AM IDT)
Stéphane Higueret(8/10/2024 4:36 PM IDT)
*Martin Thorne(8/10/2024 9:01 PM IDT)
Paul Shaw(8/10/2024 10:51 PM IDT)
*Adrian Neacsu(8/10/2024 11:06 PM IDT)
*Károly Csalogány(9/10/2024 12:03 PM IDT)
*David Greer(10/10/2024 6:40 PM IDT)
*Victor Chang(11/10/2024 12:37 AM IDT)
Guangxi Liu(11/10/2024 7:26 AM IDT)
*Ankit Aggarwal(11/10/2024 2:49 PM IDT)
*Asaf Zimmerman(11/10/2024 5:01 PM IDT)
Ashfaque Shaikh(11/10/2024 6:48 PM IDT)
Piyush Agrawal(12/10/2024 6:04 AM IDT)
Gary M. Gerken(12/10/2024 6:30 PM IDT)
Jason Kim(12/10/2024 8:59 PM IDT)
*Shouky Dan & Tamir Ganor(13/10/2024 9:28 AM IDT)
Joaquim Carrapa(13/10/2024 1:06 PM IDT)
*Stephen Ebert & Matthew Lee(15/10/2024 12:10 AM IDT)
Terry Lee(15/10/2024 3:45 AM IDT)
*Hadwin Jenkins(15/10/2024 11:37 AM IDT)
Dieter Beckerle(16/10/2024 1:23 PM IDT)
*Alper Halbutogullari(16/10/2024 1:32 PM IDT)
Michael Liepelt(16/10/2024 9:54 PM IDT)
Diana Gornea(17/10/2024 2:33 PM IDT)
*Vladimir Volevich(18/10/2024 2:18 PM IDT)
Yunkyu (James) Lee(19/10/2024 5:04 PM IDT)
Suyeong Hahn(19/10/2024 7:53 PM IDT)
Divy Soni(19/10/2024 8:09 PM IDT)
*Marco Bellocchi(20/10/2024 1:53 AM IDT)
Shirish Chinchalkar(21/10/2024 6:41 AM IDT)
Michael Oosterhagen(21/10/2024 11:26 AM IDT)
*Kang Jin Cho(21/10/2024 7:54 PM IDT)
*Erik Wünstel(21/10/2024 10:40 PM IDT)
*Mihai Stancu(22/10/2024 1:49 PM IDT)
*Nyles Heise(22/10/2024 11:07 PM IDT)
Benjamin Buhrow(23/10/2024 1:04 AM IDT)
John Spurgeon and Kipp Johnson(23/10/2024 5:41 AM IDT)
Stefan Wirth(26/10/2024 4:44 AM IDT)
Ken Dsouza(27/10/2024 10:48 AM IDT)
Frank Schoeps(27/10/2024 3:15 PM IDT)
*Franciraldo Cavalcante(28/10/2024 7:41 AM IDT)
*Dan Dima(28/10/2024 12:13 PM IDT)
*Justin Snopek(29/10/2024 12:38 AM IDT)
Benjamin Cha(29/10/2024 1:05 AM IDT)
*Motty Porat(29/10/2024 3:00 PM IDT)
*Davide Colì(30/10/2024 2:07 AM IDT)
Evan Semet(30/10/2024 6:25 AM IDT)
Ido Meisner(30/10/2024 5:53 PM IDT)
Harshit Kothari(31/10/2024 1:09 AM IDT)
Tim Walters(31/10/2024 12:06 PM IDT)
*David F.H. Dunkley(31/10/2024 12:24 PM IDT)
Alfred Reich(31/10/2024 6:20 PM IDT)
Chris Shannon(31/10/2024 7:46 PM IDT)
Maths ForFun2(31/10/2024 11:57 PM IDT)
Blaine Hill(1/11/2024 9:01 PM IDT)
*Andrea Andenna(2/11/2024 1:20 PM IDT)
Julian Ma(2/11/2024 2:27 PM IDT)
Oscar Volpatti(2/11/2024 8:14 PM IDT)