October 2019 - Challenge

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Let's assume that Alice and Bob have two (possibly the same) integer amounts of money, uniformly distributed in the [0,99] range with a minimal number of banknotes.
Using the standard US dollar banknotes denominations of 1, 5, 10, 20, and 50, if the set of notes of Alice and Bob is the same - the probability of the amount being the same is about 21%.
Your task, this month, is to find the set of five banknote denominations that uniquely determines the set with the minimal number of notes while maximizing the above probability.




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: 27/09/2019 @ 12:00 PM EST
Solution: 03/11/2019 @ 12:00 PM EST
List Updated: 16/10/2019 @ 12:00 PM EST

People who answered correctly:

Alper Halbutogullari (02/10/2019 04:25 PM IDT)
Uoti Urpala (02/10/2019 05:12 PM IDT)
Lorenz Reichel (02/10/2019 08:02 PM IDT)
Dieter Beckerle (02/10/2019 11:36 PM IDT)
Bert Dobbelaere (02/10/2019 11:53 PM IDT)
Eden Saig (03/10/2019 12:07 AM IDT)
John Reid (03/10/2019 02:24 AM IDT)
Andreas Stiller (03/10/2019 02:46 AM IDT)
David Greer (03/10/2019 04:03 AM IDT)
Sanandan Swaminathan (03/10/2019 04:25 AM IDT)
Amos Guler (03/10/2019 09:55 AM IDT)
Ayush Jain (03/10/2019 12:27 PM IDT)
Colas Kerkhove (03/10/2019 12:37 PM IDT)
James Dow Allen (03/10/2019 04:06 PM IDT)
Alex Fleischer (03/10/2019 04:36 PM IDT)
Daniel Chong Jyh Tar (03/10/2019 04:53 PM IDT)
Erik Hostens (03/10/2019 06:37 PM IDT)
Graham Hemsley (03/10/2019 07:32 PM IDT)
Calvin Pozderac (04/10/2019 12:59 AM IDT)
Collin Pearce (04/10/2019 04:00 AM IDT)
Motty Porat (04/10/2019 02:10 PM IDT)
Benjamin Lui (04/10/2019 05:58 PM IDT)
Hugo Pfoertner (04/10/2019 06:43 PM IDT)
Todd Will (04/10/2019 08:59 PM IDT)
Greg Janée (04/10/2019 09:20 PM IDT)
Florian Fischer (04/10/2019 10:59 PM IDT)
Jacoby Jaeger (05/10/2019 04:01 AM IDT)
Tamás Haba (05/10/2019 08:32 AM IDT)
Paul McKenney (05/10/2019 09:36 PM IDT)
JJ Rabeyrin (05/10/2019 10:36 PM IDT)
Keith Schneider (06/10/2019 07:45 AM IDT)
Li Li (06/10/2019 11:00 AM IDT)
Franciraldo Cavalcante (06/10/2019 07:26 PM IDT)
Yasodhar Patnaik (07/10/2019 11:25 PM IDT)
Daniel Bitin (08/10/2019 12:08 AM IDT)
Paul Revenant (08/10/2019 12:57 AM IDT)
Siegmar Szlavik (08/10/2019 02:40 AM IDT)
Fabio Michele Negroni (08/10/2019 07:32 AM IDT)
Thomas Huet (08/10/2019 08:55 AM IDT)
Harald Bögeholz (08/10/2019 01:26 PM IDT)
Vladimir Volevich (08/10/2019 01:52 PM IDT)
Stéphane Higueret (08/10/2019 06:50 PM IDT)
Guillaume Escamocher (09/10/2019 03:08 PM IDT)
Sebastian Bohm & Martí Bosch (09/10/2019 03:27 PM IDT)
Raymond Lo (09/10/2019 04:28 PM IDT)
Kang Jin Cho (09/10/2019 05:19 PM IDT)
Latchezar Christov (09/10/2019 07:39 PM IDT)
Aviv Nisgav (10/10/2019 09:28 AM IDT)
Serino Dario (10/10/2019 02:10 PM IDT)
Almog Yair (10/10/2019 06:28 PM IDT)
Clive Tong (10/10/2019 07:38 PM IDT)
Allen Kim (10/10/2019 11:30 PM IDT)
Richard Gosiorovsky (11/10/2019 08:47 AM IDT)
Wilder Boyden & Michael Leslie (11/10/2019 09:35 PM IDT)
Victor Chang (12/10/2019 07:52 PM IDT)
Dominik Reichl (13/10/2019 12:46 PM IDT)
Stanislav Grudnitskiy (13/10/2019 06:44 PM IDT)
Muhammed Halbutogullari (14/10/2019 12:23 AM IDT)
Karl D’Souza (14/10/2019 06:15 AM IDT)
Muralidhar Seshadri (14/10/2019 08:48 AM IDT)
Rustam Salikhov (14/10/2019 11:09 AM IDT)
Kevin Bauer (14/10/2019 05:45 PM IDT)
Victorien Cornet (14/10/2019 05:53 PM IDT)
Michael Liepelt (14/10/2019 07:42 PM IDT)
Dan Salajan (15/10/2019 01:37 AM IDT)
Arthur Vause (16/10/2019 0:47 AM IDT)
Peter Gerritson (16/10/2019 8:50 PM IDT)
Andrew Mullins (17/10/2019 02:40 PM IDT)
Marco Bellocchi (18/10/2019 01:38 AM IDT)
Chen Yingxiang (18/10/2019 06:03 PM IDT)
John Tromp (18/10/2019 11:50 PM IDT)
David Friedman (20/10/2019 03:07 PM IDT)
Nico Elayda (20/10/2019 09:00 PM IDT)
Branden Vennes (21/10/2019 03:09 AM IDT)
Robert Lang (21/10/2019 12:05 PM IDT)
Shouky Dan & Tamir Ganor (22/10/2019 03:51 PM IDT)
Reda Kebbaj (23/10/2019 02:40 AM IDT)
John Goh Choo Ern (25/10/2019 04:40 AM IDT)
Albert Stadler (25/10/2019 08:47 AM IDT)
Paolo Farinelli (25/10/2019 12:58 AM IDT)
Nyles Heis (26/10/2019 01:28 AM IDT)
Alistair Letcher (28/10/2019 01:26 PM IDT)