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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.

## October 2023 - Challenge

This riddle was suggested by our previous puzzlemaster, Oded Margalit. Thanks Oded!

We are entering the 26th year of Ponder This and this is the 307th riddle. Both 26 and 307 are not palindromes, but their squares 676 and 94249 are.

Your goal: Find a number n that is not a palindrome, such that n^2 is a palindrome and n \equiv 845 (\text{mod } 1201)

A Bonus "*" will be given for finding that number, such that in addition to the previous constraints, we also have n \equiv 2256 (\text{mod } 3565)

An open question that we are pondering about: Does there exist an n that is not a palindrome but n^2 is, such that all the digits of n (in base 10) are odd?

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: 28/09/2023 @ 15:30 PM EST
Solution: 05/11/2023 @ 12:00 PM EST
List Updated: 20/11/2023 @ 10:24 AM EST

#### People who answered correctly:

*Lazar Ilic(1/10/2023 11:47 AM IDT)
Paul Revenant(1/10/2023 8:21 PM IDT)
*Ariel Landau(1/10/2023 9:32 PM IDT)
Gary M. Gerken(2/10/2023 3:24 AM IDT)
*Bertram Felgenhauer(2/10/2023 6:35 AM IDT)
Nicolas Paris(2/10/2023 8:15 AM IDT)
Giorgos Kalogeropoulos(2/10/2023 1:18 PM IDT)
Richard Gosiorovsky(2/10/2023 1:32 PM IDT)
*Tim Walters(2/10/2023 5:12 PM IDT)
*Paul Revenant(2/10/2023 5:50 PM IDT)
Hakan Summakoğlu(2/10/2023 11:01 PM IDT)
*Bert Dobbelaere(2/10/2023 11:18 PM IDT)
Michał Franczak(3/10/2023 1:17 AM IDT)
*Sanandan Swaminathan(3/10/2023 4:17 AM IDT)
Kipp Johnson(3/10/2023 5:26 AM IDT)
*Dan Ismailescu(3/10/2023 5:28 AM IDT)
Lorenzo Gianferrari Pini(3/10/2023 11:03 AM IDT)
*Harald Bögeholz(3/10/2023 1:00 PM IDT)
*Yan-Wu He(3/10/2023 3:21 PM IDT)
Michael Liepelt(3/10/2023 3:58 PM IDT)
Andreas Knüpfer(3/10/2023 4:41 PM IDT)
Kipp Johnson(3/10/2023 5:45 PM IDT)
Soham Sud(3/10/2023 5:54 PM IDT)
Stéphane Higueret(3/10/2023 6:45 PM IDT)
Daniel Chong Jyh Tar(4/10/2023 4:31 PM IDT)
John Kelly(4/10/2023 5:14 PM IDT)
Daniel Stadtmauer(4/10/2023 10:52 PM IDT)
Paul Lupascu(5/10/2023 6:58 AM IDT)
Lorenzo Gianferrari Pini(5/10/2023 12:51 PM IDT)
*Alper Halbutogullari(5/10/2023 2:41 PM IDT)
*Dieter Beckerle(5/10/2023 3:27 PM IDT)
*Latchezar Christov(5/10/2023 5:28 PM IDT)
Alex Fleischer(5/10/2023 7:06 PM IDT)
Kang Jin Cho(5/10/2023 8:22 PM IDT)
*Karl Mahlburg(6/10/2023 2:43 AM IDT)
Eytan Rosenstock(6/10/2023 2:47 AM IDT)
*Franciraldo Cavalcante(6/10/2023 7:33 AM IDT)
Reda Kebbaj(6/10/2023 8:17 AM IDT)
Quentin Higueret(6/10/2023 8:34 AM IDT)
*Guglielmo Sanchini1(6/10/2023 10:13 AM IDT)
Cameron Ritson(6/10/2023 1:45 PM IDT)
*Vladimir Volevich(6/10/2023 4:04 PM IDT)
*Marco Bellocchi(7/10/2023 1:59 AM IDT)
Andreas Höglund(7/10/2023 2:54 AM IDT)
*Andrew Gauld(7/10/2023 9:43 AM IDT)
Fabio Michele Negroni(7/10/2023 1:21 PM IDT)
Peyo(7/10/2023 8:03 PM IDT)
Adrian Neacsu(7/10/2023 9:14 PM IDT)
*Aaron Kim(7/10/2023 9:49 PM IDT)
Dan Dima(8/10/2023 3:01 PM IDT)
Clive Tong(8/10/2023 3:45 PM IDT)
*Dan Dima(8/10/2023 4:32 PM IDT)
*Jeff Harris(8/10/2023 7:56 PM IDT)
Dominik Reichl(8/10/2023 8:37 PM IDT)
*David F.H. Dunkley(9/10/2023 12:40 AM IDT)
*Thomas Egense(9/10/2023 9:54 AM IDT)
*Bertram Felgenhauer(9/10/2023 12:56 PM IDT)
Matt Cristina(9/10/2023 7:05 PM IDT)
*Maksym Voznyy(10/10/2023 12:56 AM IDT)
*Dillon Davis(10/10/2023 1:39 AM IDT)
*Alfred Reich(10/10/2023 9:34 AM IDT)
*Martin Thorne(10/10/2023 11:12 PM IDT)
Daniel Bitin(11/10/2023 12:01 PM IDT)
Evert van Dijken(11/10/2023 8:42 PM IDT)
*Govind Jujare(12/10/2023 1:46 AM IDT)
Abhinav Bana(12/10/2023 8:14 AM IDT)
*Lyes Belhoul(12/10/2023 8:31 PM IDT)
*Hugo Pfoertner(12/10/2023 10:54 PM IDT)
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Florian Sikora(15/10/2023 2:55 PM IDT)
*Alain Michiels(15/10/2023 4:03 PM IDT)
Amos Guler(16/10/2023 8:01 PM IDT)
Sri Mallikarjun J(17/10/2023 5:27 PM IDT)
*Lorenz Reichel(17/10/2023 11:51 PM IDT)
*Rong Fan(18/10/2023 12:09 AM IDT)
*Julien Vincent Pradier(18/10/2023 12:16 AM IDT)
*Kabir Menghrajani(19/10/2023 6:21 AM IDT)
*Arthur Vause(19/10/2023 2:26 PM IDT)
Evan Semet(19/10/2023 5:20 PM IDT)
*David Greer(19/10/2023 6:29 PM IDT)
John Tromp(20/10/2023 2:09 PM IDT)
Guy Daniel Hadas(20/10/2023 6:16 PM IDT)
Blaine Hill(22/10/2023 11:38 PM IDT)
Isaac Greenleaf(23/10/2023 11:36 PM IDT)
*Nyles Heise(24/10/2023 5:17 AM IDT)
Armin Krauss(25/10/2023 12:12 PM IDT)
Mark Beyleveld(25/10/2023 11:07 PM IDT)
*Hans-Peter Schrei(26/10/2023 8:26 PM IDT)
Maya Farber Brodsky(27/10/2023 1:20 PM IDT)
Samuel Grondahl(27/10/2023 5:45 PM IDT)
*Chris Shannon(28/10/2023 2:43 AM IDT)
*Thomas McClave(29/10/2023 12:01 AM IDT)
Christoph Baumgarten(30/10/2023 11:23 AM IDT)
Victor Rasmussen(31/10/2023 1:41 AM IDT)
*Oscar Volpatti(1/11/2023 4:13 AM IDT)
Daniel Copeland(1/11/2023 6:48 AM IDT)
*Radu-Alexandru Todor(2/11/2023 4:00 AM IDT)
Shouky Dan & Tamir Ganor(2/11/2023 4:03 PM IDT)