# Ponder This

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## April 2020 - Challenge

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.
For example, the adjacency matrix of the graph depicted above is

```01110
10001
10010
10101
01010
```

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.

Update (3/4): We were seeking the answer of Day 19 (which can give a solution with a better approximation), but we also accepted answers for Day 10.

Update (30/4): Due to the COVID-19 crisis, with many people still isolated in their homes - we are extending April's challenge for yet another month.

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: 30/03/2020 @ 12:00 PM EST
Solution: 03/05/2020 @ 12:00 PM EST
List Updated: 25/05/2020 @ 12:00 PM EST

**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)