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2021-04-05, 16:44   #12
Dieter

Oct 2017

2×5×11 Posts

Quote:
 Originally Posted by Kebbaj Indeed it is Josephus Problem. In example 1 of the wheel with q = 5: 1 round removes the 5 2nd round remove the 3 3rd round removes the 8 and remains 1,2,3,6,7 The next round is the 7 which will jump. .... But what I don't understand is example 2. "a set of k numbers unwinnable"?
„There are no unwinnable sets for n smaller than 9“. An example:

n=8, k=4=number of spins. When the player chooses a number q and makes 4 spins, he gets a combination of 4 different numbers between 1 and 8. When he chooses another q, he gets perhaps another combination - or the same combination.
There are (8 choose 4) = 70 such combinations. All are reachable, if you ckeck enough values for q.
But:
Example n=9 und k=4. There are 126 possible quintetts of values. But this time, only 123 of these values are reachable - (1,2,5,8,9) and (2,3,4,5,8) and (2,5,6,7,8) are not reachable. Just for fun I checked 1<=q<=10000000 - no chance .
These three combinations are "unwinnable sets".

 2021-04-05, 16:55 #13 Dieter   Oct 2017 2·5·11 Posts In the challenge sometimes k is the number of spins and sometimes k is the number of elements in the remaining sets. For the number of possibilities that doesn‘t make a difference, because (n choose k) = (n choose (n-k)). For comparing: If my code works correctly, to get the 123 in example 2 I need more than 400 as limit for q.
2021-04-06, 19:13   #14
Kebbaj

"Kebbaj Reda"
May 2018
Casablanca, Morocco

10100012 Posts

Quote:
 Originally Posted by Dieter „There are no unwinnable sets for n smaller than 9“. An example: n=8, k=4=number of spins. When the player chooses a number q and makes 4 spins, he gets a combination of 4 different numbers between 1 and 8. When he chooses another q, he gets perhaps another combination - or the same combination. There are (8 choose 4) = 70 such combinations. All are reachable, if you ckeck enough values for q. But: Example n=9 und k=4. There are 126 possible quintetts of values. But this time, only 123 of these values are reachable - (1,2,5,8,9) and (2,3,4,5,8) and (2,5,6,7,8) are not reachable. Just for fun I checked 1<=q<=10000000 - no chance . These three combinations are "unwinnable sets".
Frankly, it is you dieter who should write the challenge, I understand perfectly the example 2, and I found all the combinaisons :
"70 combinations for the 8".
"126 possible quintetts of values"
(1,2,5,8,9) (2,3,4,5,8) (2,5,6,7,8). Not reachable.
Now i am in the process of resolving the question. !

..
Thanks.

2021-04-07, 05:20   #15
Dieter

Oct 2017

1568 Posts

Quote:
 Originally Posted by Kebbaj Frankly, it is you dieter who should write the challenge, I understand perfectly the example 2, and I found all the combinaisons : "70 combinations for the 8". "126 possible quintetts of values" (1,2,5,8,9) (2,3,4,5,8) (2,5,6,7,8). Not reachable. Now i am in the process of resolving the question. ! .. Thanks.
I only repeated this part of the challenge with other words. If A explains anything to C and B explains the same matter using other words, B always has an advantage to be understood!
I admire the puzzlemasters for their ideas.

2021-04-07, 08:01   #16
Kebbaj

"Kebbaj Reda"
May 2018
Casablanca, Morocco

34 Posts

Quote:
 Originally Posted by Kebbaj Indeed it is Josephus Problem. In example 1 of the wheel with q = 5: 1 round removes the 5 2nd round remove the 3 3rd round removes the 8 and remains 1,2,3,6,7 The next round is the 7 which will jump. .... But what I don't understand is example 2. "a set of k numbers unwinnable"?
You are right dieter, having this advantage here of reexplaining in more detail is an additional advantage that you did not have. Sometimes I understand very quickly, and sometimes my brain crashes.
This time it's google translate which played a trick on me. By translating into French.
Wrong translation:
"he will not be able to win exactly this set after n-k spins.
"il ne pourra pas gagner exactement cet ensemble après nk tours"

nk: 9 * 5 = 45 turns that blocked me. And I did not reread the English version. ( je sents mieux les choses en Français).

I know that if I block the first day of the puzzle, it's gone for a total block.

Last fiddled with by Kebbaj on 2021-04-07 at 08:11

2021-04-09, 23:49   #17
Kebbaj

"Kebbaj Reda"
May 2018
Casablanca, Morocco

34 Posts
visualization of example

josephus problem
I made a video visualization of example 1:

https://youtu.be/vdRDmy_tou4
Attached Files
 IBM Ponther This April 2021 Exemple 1.pdf (81.0 KB, 9 views) IBM Ponther This April 2021 unwinable sets Exemple 2.pdf (75.7 KB, 9 views)

Last fiddled with by Kebbaj on 2021-04-09 at 23:58

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