September 2019 - Challenge

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The US dollar has five common banknote denominations: 1, 5, 10, 20, and 50.
Each integer dollar value between 0 and 99 dollars can be paid in a unique way with a minimal number of notes.
If Alice and Bob each have different amounts of money, they still can have the same set of notes.
For example, if Alice has $92 and Bob has $74 (in a minimal number of notes), they both have the same set of banknotes {1,20,50}.
Let's assume that Alice and Bob have two different random amounts of money uniformly distributed in the [0,99] range with a minimal number of banknotes.
The probability that they have the same set of banknotes is approximately 3.79798%.

Your task, this month, is to find another set of five banknotes such that:

  1. Each integer dollar value between 0 and 99 dollars can be paid in a unique way with a minimal number of notes; and
  2. The probability above (same set of banknotes for two different random amounts of money uniformly distributed in the [0,99] range) would be exactly 4%.



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Challenge: 04/09/2019 @ 12:00 PM EST
Solution: 03/10/2019 @ 12:00 PM EST
List Updated: 07/10/2019 @ 12:00 PM EST

People who answered correctly:

Alex Fleischer (05/09/2019 11:12 AM IDT)
Alper Halbutogullari (09/09/2019 03:23 AM IDT)
Gary M. Gerken (09/09/2019 07:43 AM IDT)
Reiner Martin (09/09/2019 01:03 PM IDT)
John Goh (09/09/2019 02:06 PM IDT)
Guillaume Escamocher (09/09/2019 04:42 PM IDT)
Almog Yair (09/09/2019 05:26 PM IDT)
Lachezar Hristov (09/09/2019 06:24 PM IDT)
Daniel Oliveira (09/09/2019 07:36 PM IDT)
Uoti Urpala (09/09/2019 08:19 PM IDT)
Bert Dobbelaere (09/09/2019 10:23 PM IDT)
Tero Patana (10/09/2019 03:51 AM IDT)
Hugo Pfoertner (10/09/2019 04:15 AM IDT)
Jacoby Jaeger (10/09/2019 04:48 AM IDT)
Doug Miller (10/09/2019 04:59 AM IDT)
Daniel Chong Jyh Tar (10/09/2019 05:35 AM IDT)
Ariel Landau (10/09/2019 05:37 AM IDT)
Eden Saig (10/09/2019 07:23 AM IDT)
Tamás Haba (10/09/2019 09:59 AM IDT)
Thomas Huet (10/09/2019 11:17 AM IDT)
Arthur Vause (10/09/2019 11:32 AM IDT)
Todd Will (10/09/2019 05:35 PM IDT)
Dieter Beckerle (10/09/2019 06:45 PM IDT)
JJ Rabeyrin (10/09/2019 10:17 PM IDT)
Lorenz Reichel (10/09/2019 10:19 PM IDT)
Daniel Bitin (10/09/2019 11:27 PM IDT)
Pål Hermunn Johansen (11/09/2019 02:17 AM IDT)
Joseph Berman (11/09/2019 03:59 AM IDT)
Tom Chen (11/09/2019 05:37 AM IDT)
David Friedman (11/09/2019 06:06 AM IDT)
Victor Chang (11/09/2019 09:35 AM IDT)
John Tromp (11/09/2019 02:46 PM IDT)
Graham Hemsley (11/09/2019 06:25 PM IDT)
Ilya Tarygin (11/09/2019 07:36 PM IDT)
Jingran Lin (12/09/2019 12:47 AM IDT)
Siegmar Szlavik (12/09/2019 02:32 AM IDT)
Joaquim Neves Carrapa (12/09/2019 03:48 AM IDT)
Ralf Jonas (12/09/2019 08:39 AM IDT)
Michael Liepelt (12/09/2019 09:28 AM IDT)
Stanislav Grudnitskiy (12/09/2019 11:51 AM IDT)
Vladimir Volevich (12/09/2019 05:31 PM IDT)
Benjamin Lui (12/09/2019 07:02 PM IDT)
James Dow Allen (13/09/2019 12:29 AM IDT)
Kang Jin Cho (13/09/2019 02:30 PM IDT)
David Greer (13/09/2019 03:46 PM IDT)
Florian Fischer (14/09/2019 01:17 AM IDT)
Xiuhan Wang (16/09/2019 06:48 AM IDT)
Serge Thill (17/09/2019 01:00 PM IDT)
Harald Bögeholz (17/09/2019 06:02 AM IDT)
Omer Shechter (16/09/2019 06:40 PM IDT)
Victorien Cornet (17/09/2019 03:49 PM IDT)
Nico Elayda (17/09/2019 07:50 PM IDT)
Muhammed Halbutogullari (17/09/2019 10:30 PM IDT)
Allen Kim (17/09/2019 11:23 PM IDT)
Hyung Sik Hwang (18/09/2019 01:20 PM IDT)
Alexey Zyl (18/09/2019 08:25 PM IDT)
Móra Péter (18/09/2019 10:44 PM IDT)
Reda Kebbaj (19/09/2019 12:22 AM IDT)
Sanandan Swaminathan (19/09/2019 03:47 AM IDT)
Greg Janée (19/09/2019 06:23 AM IDT)
Calvin Pozderac (19/09/2019 07:02 AM IDT)
Andy Greig (19/09/2019 10:29 AM IDT)
Andreas Stiller (19/09/2019 01:35 PM IDT)
John Reid (19/09/2019 03:16 PM IDT)
Rustam Salikhov (19/09/2019 05:23 PM IDT)
Dan Salajan (19/09/2019 06:49 PM IDT)
Zhongxing Xue (19/09/2019 09:32 PM IDT)
Yasodhar Patnaik (20/09/2019 01:55 AM IDT)
Ayush Jain (20/09/2019 09:27 AM IDT)
Marco Bellocchi (21/09/2019 12:43 AM IDT)
Daniel Blazewicz (21/09/2019 01:05 AM IDT)
Ken Dsouza (21/09/2019 08:39 AM IDT)
Mathias Schenker (21/09/2019 12:09 PM IDT)
Mark Rickert (21/09/2019 12:53 PM IDT)
Andrew Mullins (22/09/2019 09:53 AM IDT)
Amos Guler (22/09/2019 12:18 PM IDT)
Luke Pebody (23/09/2019 01:14 PM IDT)
Emir Haleva (23/09/2019 06:00 PM IDT)
Nyles Heise (24/09/2019 08:37 AM IDT)
Tyler Mullen (24/09/2019 01:26 PM IDT)
Paul Revenant (25/09/2019 03:50 PM IDT)
Erik Wünstel (25/09/2019 05:12 PM IDT)
Bin Liu (25/09/2019 05:19 PM IDT)
Rudy Cortembert (26/09/2019 02:54 PM IDT)
Kai Guttmann (26/09/2019 10:48 PM IDT)
Daniel Showalter (26/09/2019 11:44 PM IDT)
Dan Dima (28/09/2019 11:41 PM IDT)
Peter Gerritson (28/09/2019 11:57 PM IDT)
Dominik Reichl (28/09/2019 01:14 PM IDT)
Clive Tong (28/09/2019 04:30 PM IDT)
Hrushikesh Tilak (29/09/2019 09:07 AM IDT)
Fabio Negroni (29/09/2019 01:48 PM IDT)
Shouky Dan & Tamir Ganor (29/09/2019 06:14 PM IDT)
Motty Porat (30/09/2019 12:09 AM IDT)
Piyush Agrawal (30/09/2019 03:36 PM IDT)
Colas Kerkhove (30/09/2019 07:04 PM IDT)
Michael Chirozzi (01/10/2019 12:21 AM IDT)
Damien Devlies (01/10/2019 10:17 AM IDT)
Radu-Alexandru Todor (01/10/2019 12:38 PM IDT)
Franciraldo Cavalcante (01/10/2019 05:09 PM IDT)
Oscar Volpatti (01/10/2019 05:46 PM IDT)
Klaus Hoffmann (01/10/2019 06:44 PM IDT)
Albert Stadler (02/10/2019 01:12 PM IDT)
Wilder Boyden & Andrew Melendez (03/10/2019 01:56 AM IDT)
Collin Pearce (03/10/2019 08:23 AM IDT)
Erik Hostens (03/10/2019 02:19 PM IDT)
Martí Bosch (03/10/2019 04:43 PM IDT)
Stéphane Higueret (04/10/2019 11:06 PM IDT)
David F.H. Dunkley (06/10/2019 10:20 AM IDT)
Li Li (06/10/2019 11:00 AM IDT)