Ponder This Challenge - April 2020 - COVID-19 outbreak

This month's challenge is inspired by the COVID-19 pandemic.
Suppose that the world has five cities and they are all connected to one another as depicted by the five-verticed graph in the following picture:

Let's assume that the infection passes daily along the edges. So, if on day t, "D" is infected and "C" is healthy, then "C" has a 10% chance of getting infected, by "D", on day t+1.
If "A" is infected at time 0, after ten days, there is about a 29.16521896% probability that all five will be infected.

Find a graph with no more than eight vertices that gives a probability of 70.00% (accurate to the second decimal digit after the decimal point) of all cities/vertices being infected after ten days.
Give your answer as an adjacency matrix.
For example, the adjacency matrix of the graph depicted above is

Bonus '*' for getting the closest to 70% in 19 days; and ’**' for getting even closer. Current best is less than 1.9E-7 away from 0.7.

Solution

• Click here to view the solution

  We were seeking the answer of Day 19, where writing PT (Ponder This):

  01110111
  10110010
  11010010
  11101000
  00010100
  10001000
  11100010
  10000000
  

  gives a solution of 0.7000146451.
  However, we've also accepted solutions that give ~70.007% after 10 days, such as:

  01101010
  10000001
  10010010
  00101001
  10010100
  00001010
  10100101
  01010010
  

  Benjamin Lui found a 69.995% solution with only seven vertices:

  0111000
  1011110
  1100100
  1100100
  0111011
  0100101
  0000110
  

  Alper Halbutogullari was the first to find a solution that after 19 steps gets to ~70.0000865%:

  01101010
  10000001
  10010010
  00101001
  10010100
  00001010
  10100101
  01010010
  

  Florian Fischer sent us a drawing (thanks)

  Haye Chan found the best approximation (69.999981%) for seven cities and 28 days:

  0000100
  0001111
  0000111
  0100110
  1111000
  0111000
  0110000
  

  and Arthur Vause found a solution of 70.000002195% for 9 cities and 34 days:

  000000010
  000010101
  000101101
  001001100
  010000011
  001100010
  011100001
  100011000
  011010100
  

  Thanks to Alok Menghrajani for his writeup.

Solvers

• **Uoti Urpala (30/03/2020 11:16 AM IDT)
• *Alper Halbutogullari (30/03/2020 04:15 PM IDT)
• JJ Rabeyrin (30/03/2020 05:08 PM IDT)
• **Bert Dobbelaere (30/03/2020 07:39 PM IDT)
• Lorenz Reichel (30/03/2020 10:09 PM IDT)
• *Latchezar Christov (01/04/2020 04:05 PM IDT)
• Willem Hendriks (01/04/2020 09:19 PM IDT)
• Mathias Schenker (01/04/2020 09:37 PM IDT)
• **Glauber Guarinello (31/03/2020 05:52 AM IDT)
• *Collin Pearce (02/04/2020 02:51 AM IDT)
• Henrique Fiuza (02/04/2020 03:07 AM IDT)
• **Deron Stewart (02/04/2020 03:10 AM IDT)
• *Anders Kaseorg (02/04/2020 06:35 AM IDT)
• Graham Hemsley (02/04/2020 12:23 PM IDT)
• Guillermo Wildschut (02/04/2020 02:41 PM IDT)
• Lorenzo Gianferrari Pini (02/04/2020 07:09 PM IDT)
• *Joerg Schepers (02/04/2020 11:01 PM IDT)
• Eden Saig (03/04/2020 01:28 AM IDT)
• *Todd Will (03/04/2020 02:06 PM IDT)
• Reiner Martin (04/04/2020 03:15 AM IDT)
• **Arthur Vause (05/04/2020 09:35 AM IDT)
• *David Greer (05/04/2020 01:53 PM IDT)
• **Dimas Ramos (05/04/2020 06:48 PM IDT)
• Tyler Mullen (06/04/2020 03:38 AM IDT)
• Paul Revenant (06/04/2020 10:46 AM IDT)
• Li Wang (06/04/2020 01:52 PM IDT)
• Clive Tong (06/04/2020 08:12 PM IDT)
• *Dan Dima (07/04/2020 12:10 PM IDT)
• Benjamin Lui (07/04/2020 05:01 PM IDT)
• Erik Hostens (07/04/2020 11:09 PM IDT)
• **Kang Jin Cho (08/04/2020 12:13 PM IDT)
• **Oscar Volpatti (08/04/2020 05:09 PM IDT)
• *Chris Shannon (08/04/2020 11:13 PM IDT)
• *Khaled Fayed (10/04/2020 04:22 AM IDT)
• **Vladimir Volevich (10/04/2020 09:26 AM IDT)
• **Bertram Felgenhauer (10/04/2020 11:21 AM IDT)
• Mathieu Roget (10/04/2020 12:14 PM IDT)
• Keith Schneider (10/04/2020 05:23 PM IDT)
• **Haye Chan (11/04/2020 01:21 PM IDT)
• *Andreas Puccio (11/04/2020 05:30 PM IDT)
• *Tommy Pensyl (12/04/2020 06:30 AM IDT)
• *James Dow Allen (12/04/2020 03:02 PM IDT)
• *Walter Schmidt (12/04/2020 03:45 PM IDT)
• *Nyles Heise (13/04/2020 07:03 AM IDT)
• *Walter Sebastian Gisler (13/04/2020 09:43 AM IDT)
• **Stephen Herbert Jr (13/04/2020 02:46 PM IDT)
• Daniel Bitin (13/04/2020 05:09 PM IDT)
• *Greg Janée (13/04/2020 10:55 PM IDT)
• *Yongxing Jim Wang (14/04/2020 02:56 AM IDT)
• *Jacoby Jaeger (14/04/2020 06:09 AM IDT)
• Victor Chang (15/04/2020 07:10 AM IDT)
• *Andrew Mullins (17/04/2020 10:20 AM IDT)
• John Goh (18/04/2020 08:23 PM IDT)
• **Florian Fischer (21/04/2020 01:36 PM IDT)
• *Yuxuan Shui (20/04/2020 12:47 AM IDT)
• Shouky Dan & Tamir Ganor (20/04/2020 09:38 PM IDT)
• *Marco Bellocchi (24/04/2020 09:27 AM IDT)
• Stefan Wirth (24/04/2020 05:59 PM IDT)
• **Alok Menghrajani (24/04/2020 07:16 PM IDT)
• Alex Fleischer (24/04/2020 10:37 PM IDT)
• *Jonah Mann (25/04/2020 03:31 PM IDT)
• Diana Gornea & Bogdan Posa (26/04/2020 01:28 AM IDT)
• Pern Jie Quah (26/04/2020 04:21 AM IDT)
• Jim Clare (26/04/2020 05:08 PM IDT)
• *Dipto Thakurta (26/04/2020 09:02 PM IDT)
• Hugo Pfoertner (27/04/2020 04:25 PM IDT)
• *David Friedman (27/04/2020 06:17 AM IDT)
• *Dieter Beckerle (27/04/2020 07:32 AM IDT)
• *Stanislav Grudnitskiy (28/04/2020 05:08 PM IDT)
• *Karl D’Souza (28/04/2020 11:04 PM IDT)
• *David F.H. Dunkley (30/04/2020 12:49 AM IDT)
• Radu-Alexandru Todor (30/04/2020 01:04 AM IDT)
• Ken Dsouza (30/04/2020 08:09 AM IDT)
• Sebastian Bohm & Martí Bosch (30/04/2020 10:49 AM IDT)
• Kai Guttmann (30/04/2020 06:48 PM IDT)
• *Paolo Farinelli (30/04/2020 09:37 PM IDT)
• **Li Li (01/05/2020 07:54 AM IDT)
• *Daniel Chong Jyh Tar (01/05/2020 09:45 PM IDT)
• Ben Roberts (02/05/2020 09:26 AM IDT)
• Fabio Negroni (19/05/2020 08:31 AM IDT)
• Alessandro Marzo (19/05/2020 01:39 PM IDT)
• Reda Kebbaj (24/05/2020 12:55 AM IDT)