Ponder This Challenge - February 2016 - IBM InterConnect

Ponder This Challenge:

This month's challenge is about IBM's InterConnect 2016 conference.

Assign each letter a different digit such that the following mathematical equations would be correct (** denotes exponentiation):

a**connect = c (mod inter)

a**connect = a**toe (mod at)

a**connect = a**toe (mod cm)

n**i = ban

Hint: By guessing a little, this can almost be entirely solved without using a computer.

For a bonus '*', what is the connection of the solution to "XCF MODULE ID FILTER NOT ACCEPTED"?

Solution

• Click here to view the solution

  The number of possibilities (10!=3,628,800) is well in the range of brute force checking, but we wanted to make it almost doable without a computer.
  Here is Hao Zheng's solution
  Steps:

  1. Using n**i = ban to get the following possible solutions of n, i, b, a
     2^9 = 512 (n, i, b, a) = (2, 9, 5, 1) <-- eliminated by step 2
     3^5 = 243 (n, i, b, a) = (3, 5, 2, 4)
     5^3 = 125 (n, i, b, a) = (5, 3, 1, 2)
     5^4 = 625 (n, i, b, a) = (5, 4, 6, 2)
     6^3 = 216 (n, i, b, a) = (6, 3, 2, 1) <-- eliminated by step 2
     9^3 = 729 (n, i, b, a) = (9, 3, 7, 2)

  2. Using a**connect = c (mod inter) to eliminate a = 1, otherwise a = c = 1

  3. There are 4 possible solutions for n, i, b, a
     (3, 5, 2, 4)
     (5, 3, 1, 2)
     (5, 4, 6, 2)
     (9, 3, 7, 2)
     Notice that c and t cannot be 0 because they are the leading digits.
     So the number of all possible solutions for
     (a, b, c, e, i, m, n, o, r, t)
     is 4 * 5 * 4 * 4 * 3 * 2 * 1 = 1920
     Write a program to try all the 1920 possibilities, we get the following
     (a, b, c, e, i, m, n, o, r, t) =
     (2, 6, 8, 0, 4, 9, 5, 1, 7, 3)

  But there was another clue: connect = toe (mod 11) (left as an exercise for the reader: David Greer noticed that part). So a**connect = a**toe (mod 2**11-1), which is 2047=89*23, which helps guessing that cm=89 and at=23, leaving a few possibilities to check.

  As for the bonus, the error message "XCF MODULE ID FILTER NOT ACCEPTED" is IXC469I and converting 469 to letters, using the solution, yields "IBM".

Solvers

• Daniel Bitin (28/01/2016 05:39 PM IDT)
• Robert Gerbicz (28/01/2016 05:46 PM IDT)
• Jean-Baptiste Rouquier (28/01/2016 06:19 PM IDT)
• Lorenz Reichel (28/01/2016 06:49 PM IDT)
• *Armin Krauss (28/01/2016 11:18 PM IDT)
• Andreas Stiller (29/01/2016 12:49 AM IDT)
• Jimmy Waters (29/01/2016 01:34 AM IDT)
• Radu-Alexandru Todor (29/01/2016 01:43 AM IDT)
• Hao Zheng (29/01/2016 03:44 AM IDT)
• Nicolas Bitouze (29/01/2016 06:21 AM IDT)
• Yan-Wu He (29/01/2016 03:43 PM IDT)
• *Lewis Chen (29/01/2016 03:57 PM IDT)
• *Francis Golding (29/01/2016 04:10 PM IDT)
• Kang Jin Cho (29/01/2016 04:51 PM IDT)
• *Donald T Dodson (29/01/2016 10:03 PM IDT)
• Brendan Berger (29/01/2016 10:11 PM IDT)
• Alex Fleischer (30/01/2016 10:53 AM IDT)
• Shirish Chinchalkar (30/01/2016 04:40 PM IDT)
• Harald Bögeholz (30/01/2016 08:34 PM IDT)
• Todd Will (31/01/2016 12:25 AM IDT)
• Peter Gerritson (31/01/2016 05:29 AM IDT)
• Wang Gangyi (31/01/2016 09:23 AM IDT)
• Claudio Hüni (31/01/2016 11:35 AM IDT)
• Fabio Michele Negroni (31/01/2016 01:36 PM IDT)
• Aviv Nisgav (31/01/2016 05:22 PM IDT)
• Kwonil Kobe Ko (31/01/2016 07:01 PM IDT)
• *Ajay Mallepally (31/01/2016 07:08 PM IDT)
• Kipp Johnson (31/01/2016 08:55 PM IDT)
• *Gary M. Gerken (31/01/2016 09:37 PM IDT)
• Sergey Koposov (01/02/2016 02:03 AM IDT)
• *Stéphane Higueret (01/02/2016 02:53 PM IDT)
• Joseph DeVincentis (01/02/2016 04:17 PM IDT)
• Minxi Jiang (01/02/2016 05:05 PM IDT)
• Raymond Lo (01/02/2016 06:17 PM IDT)
• Nadir S (01/02/2016 09:50 PM IDT)
• Pål Hermunn Johansen (01/02/2016 10:03 PM IDT)
• *Motty Porat (01/02/2016 11:56 PM IDT)
• *David F. H. Dunkley (02/02/2016 12:18 AM IDT)
• Victor Chang (02/02/2016 02:38 AM IDT)
• Scott Abbey (02/02/2016 03:05 AM IDT)
• Arsene Lui (02/02/2016 08:22 AM IDT)
• *Arthur Vause (02/02/2016 11:46 AM IDT)
• Tomáš Jurík (02/02/2016 01:06 PM IDT)
• Roberto Tauraso (02/02/2016 01:57 PM IDT)
• *Rudy Cortembert (02/02/2016 03:57 PM IDT)
• *Chris Lewis (02/02/2016 05:09 PM IDT)
• Franciraldo Cavalcante (02/02/2016 07:46 PM IDT)
• *Kevin Petrychyn (02/02/2016 10:26 PM IDT)
• Gida Pataki (03/02/2016 01:47 AM IDT)
• Steven Langerwerf (03/02/2016 06:41 PM IDT)
• Di Luo (04/02/2016 08:22 AM IDT)
• Jan Rothkegel (04/02/2016 09:31 AM IDT)
• Guang-Zhong Sun (04/02/2016 10:38 AM IDT)
• Hamidreza Bidar (04/02/2016 12:50 PM IDT)
• Mathias Schenker (04/02/2016 03:50 PM IDT)
• *Jonathan David Johnston (04/02/2016 05:19 PM IDT)
• *Martin Thiim (04/02/2016 05:26 PM IDT)
• David Friedman (04/02/2016 11:42 PM IDT)
• Ali Can Keserel (05/02/2016 02:07 PM IDT)
• Matthias Bussas (05/02/2016 03:59 PM IDT)
• *Paolo Farinelli (05/02/2016 07:24 PM IDT)
• *Lawrence Hon (06/02/2016 07:01 PM IDT)
• Matt Falk (07/02/2016 06:00 AM IDT)
• Adrian Neacsu (07/02/2016 05:41 PM IDT)
• Liubing Yu (07/02/2016 05:58 PM IDT)
• Tahsin Erdal Berk (08/02/2016 02:20 PM IDT)
• *Stefano Leucci (08/02/2016 04:39 PM IDT)
• Kautil Reddy (08/02/2016 04:57 PM IDT)
• *Michael Rosola (09/02/2016 04:08 AM IDT)
• José Eduardo Gaboardi de Carvalho (09/02/2016 06:04 PM IDT)
• Albert Stadler (09/02/2016 10:01 PM IDT)
• Larry Kearney (10/02/2016 03:10 AM IDT)
• *Emir Haleva (10/02/2016 11:11 AM IDT)
• Tim Cieplowski (11/02/2016 04:55 AM IDT)
• *Shouky Dan & Tamir Ganor (11/02/2016 12:53 PM IDT)
• Beni Bachmann (11/02/2016 11:59 PM IDT)
• Junjiajia Long (12/02/2016 08:21 AM IDT)
• Zoltan Haindrich (14/02/2016 01:22 AM IDT)
• Hyun Min Victoria Woo (15/02/2016 12:51 AM IDT)
• Dieter Beckerle (16/02/2016 12:35 PM IDT)
• J. Eric Ivancich (16/02/2016 04:41 PM IDT)
• *Rahul Upakare (16/02/2016 07:27 PM IDT)
• *Enis Berk Çoban (17/02/2016 08:00 PM IDT)
• Yuval Salant (17/02/2016 10:47 PM IDT)
• *Mohamed Elsharnouby (18/02/2016 10:17 AM IDT)
• *Karim Alaoui (19/02/2016 02:55 PM IDT)
• Grant Boudreaux (19/02/2016 04:27 PM IDT)
• Erik Wünstel (19/02/2016 07:34 PM IDT)
• *Anders Bisbjerg Madsen (19/02/2016 08:21 PM IDT)
• *Akshay G. Joshi (21/02/2016 10:13 PM IDT)
• David Greer (23/02/2016 12:59 AM IDT)
• Tilo Anschütz (24/02/2016 09:10 PM IDT)
• Adrian Toncean (25/02/2016 09:05 AM IDT)
• *Amir Sarid (26/02/2016 09:11 PM IDT)
• Nyles Heise (27/02/2016 04:07 AM IDT)
• Alain Stephan (27/02/2016 06:05 PM IDT)
• *Benjamin Lui (27/02/2016 07:23 PM IDT)
• Zhou Ding Wen (28/02/2016 07:41 AM IDT)
• *Jörg Binder (28/02/2016 06:34 PM IDT)
• Martin Sergio H. Faester (28/02/2016 08:18 PM IDT)
• Oscar Volpatti (01/03/2016 10:19 AM IDT)
• Mihail-Iulian Plesa (01/03/2016 06:13 PM IDT)