mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Puzzles (https://www.mersenneforum.org/forumdisplay.php?f=18)

 Xyzzy 2021-02-01 16:03

February 2021

[url]https://www.research.ibm.com/haifa/ponderthis/challenges/February2021.html[/url]

 Kebbaj 2021-02-03 00:19

1 Attachment(s)
the first people vaccinated by itself ?

 Dieter 2021-02-03 09:11

[QUOTE=Kebbaj;570768]the first people vaccinated by itself ?[/QUOTE]
That are 17 people. I have 39.
Example:
(4/1) has only (5/1) as trusted neighbour. (5/1) is vaccinated. So /4/1) will get vaccinated, too - if my understanding of the challenge is ok.

 SmartMersenne 2021-02-03 10:23

The following people would be vaccinated with no additional convincing other than what is given in the question:

101011000011
100000000001
100100000001
110001000001
100001000001
100000011100
100000011000
000000000000
000000000000
000000101101
100000000001
101110110101

 Dieter 2021-02-03 11:29

[QUOTE=SmartMersenne;570790]The following people would be vaccinated with no additional convincing other than what is given in the question:

101011000011
100000000001
100100000001
110001000001
100001000001
100000011100
100000011000
000000000000
000000000000
000000101101
100000000001
101110110101[/QUOTE]
That's exactly my result.

 SmartMersenne 2021-02-03 15:21

Here is a solution set with 60 elements:

{(4,7),(6,1),(5,3),(4,4),(7,5),(2,7),(6,2),(6,5),(12,7),(2,11),(4,6),(3,9),(3,2),(9,12),(9,11),(5,2),(6,7),(2,4),(6,3),(11,2),(2,10),(7,10),(10,6),(9,4),(10,8),(9,5),(2,12),(7,9),(4,5),(7,7),(9,1),(4,12),(4,2),(7,4),(2,5),(9,2),(6,11),(11,5),(5,5),(11,3),(9,9),(10,12),(7,8),(4,8),(10,4),(8,10),(7,6),(2,2),(5,9),(11,11),(8,9),(3,6),(8,2),(7,12),(12,4),(3,5),(11,8),(10,10),(4,11),(12,6)}

If you start with this set, everyone will get vaccinated after very convincing conversations. :smile:

 Kebbaj 2021-02-03 23:41

[QUOTE=Dieter;570787]That are 17 people. I have 39.
Example:
(4/1) has only (5/1) as trusted neighbour. (5/1) is vaccinated. So /4/1) will get vaccinated, too - if my understanding of the challenge is ok.[/QUOTE]

I'm talking about the following sentence:
(If the set of trusted neighbors is empty, that person is already convinced and gets vaccinated without further convincing.)
which gives 17 person self vacineted.
For exemple:
0
x0
0

After those who have only one convicton with these 17 will be vaccinated and then become 39 without our inetvention.
I confirm I have the same configuration of 39 people.

 Kebbaj 2021-02-04 00:33

[QUOTE=SmartMersenne;570793]Here is a solution set with 60 elements:

{(4,7),(6,1),(5,3),(4,4),(7,5),(2,7),(6,2),(6,5),(12,7),(2,11),(4,6),(3,9),(3,2),(9,12),(9,11),(5,2),(6,7),(2,4),(6,3),(11,2),(2,10),(7,10),(10,6),(9,4),(10,8),(9,5),(2,12),(7,9),(4,5),(7,7),(9,1),(4,12),(4,2),(7,4),(2,5),(9,2),(6,11),(11,5),(5,5),(11,3),(9,9),(10,12),(7,8),(4,8),(10,4),(8,10),(7,6),(2,2),(5,9),(11,11),(8,9),(3,6),(8,2),(7,12),(12,4),(3,5),(11,8),(10,10),(4,11),(12,6)}

If you start with this set, everyone will get vaccinated after very convincing conversations. :smile:[/QUOTE]
I checked your 60-item solution,everyone will get vaccinated after very convincing conversations! A lot of negotiation after conviction.
There is much less than 60.

 SmartMersenne 2021-02-04 02:10

[QUOTE=Kebbaj;570812]I checked your 60-item solution,everyone will get vaccinated after very convincing conversations! A lot of negotiation after conviction.
There is much less than 60.[/QUOTE]

Here is one with 50 items:

{(11,6),(3,2),(10,11),(2,6),(5,11),(10,10),(11,3),(6,1),(4,12),(7,11),(2,3),(9,12),(11,11),(5,2),(3,4),(9,5),(8,8),(2,5),(10,6),(8,12),(8,4),(2,10),(10,9),(6,11),(2,12),(2,7),(4,9),(5,5),(11,9),(4,8),(7,5),(1,4),(7,10),(8,10),(3,5),(8,11),(4,3),(10,12),(3,11),(3,10),(6,4),(4,6),(9,10),(11,7),(12,4),(9,8),(7,12),(5,8),(9,2),(6,3)}

 Kebbaj 2021-02-04 08:56

[QUOTE=SmartMersenne;570817]Here is one with 50 items:

{(11,6),(3,2),(10,11),(2,6),(5,11),(10,10),(11,3),(6,1),(4,12),(7,11),(2,3),(9,12),(11,11),(5,2),(3,4),(9,5),(8,8),(2,5),(10,6),(8,12),(8,4),(2,10),(10,9),(6,11),(2,12),(2,7),(4,9),(5,5),(11,9),(4,8),(7,5),(1,4),(7,10),(8,10),(3,5),(8,11),(4,3),(10,12),(3,11),(3,10),(6,4),(4,6),(9,10),(11,7),(12,4),(9,8),(7,12),(5,8),(9,2),(6,3)}[/QUOTE]

The next answer you will say 40 element?:smile:
I give it by optimizing your solution to 40:
{(4,9),(7,5),(11,3),(4,12),(7,11),(11,6),(3,11),(6,3),(10,9),(3,5),(6,4),(10,6),(3,4),(6,11),(10,10),(3,2),(6,1),(10,11),(2,7),(5,8),(9,2),(2,12),(5,5),(9,8),(2,5),(5,2),(9,5),(2,3),(12,4),(4,6),(8,10),(2,6),(11,7),(4,3),(8,4),(1,4),(11,9),(4,8),(8,8),(11,11)}

Who says 30?

 SmartMersenne 2021-02-04 12:58

Let's not spoil the problem

[QUOTE=Kebbaj;570833]The next answer you will say 40 element?:smile:
I give it by optimizing your solution to 40:
{(4,9),(7,5),(11,3),(4,12),(7,11),(11,6),(3,11),(6,3),(10,9),(3,5),(6,4),(10,6),(3,4),(6,11),(10,10),(3,2),(6,1),(10,11),(2,7),(5,8),(9,2),(2,12),(5,5),(9,8),(2,5),(5,2),(9,5),(2,3),(12,4),(4,6),(8,10),(2,6),(11,7),(4,3),(8,4),(1,4),(11,9),(4,8),(8,8),(11,11)}

Who says 30?[/QUOTE]

OK, let's stop here before one of us solves the problem and reveals the answer. :smile:

All times are UTC. The time now is 14:15.