[QUOTE=Kebbaj;575253]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"?[/QUOTE]
„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".

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.

[QUOTE=Dieter;575261]„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".[/QUOTE]

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.

[QUOTE=Kebbaj;575353]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.[/QUOTE]
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.

[QUOTE=Kebbaj;575253]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"?[/QUOTE]

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.

visualization of example
 

josephus problem
I made a video visualization of example 1:

[url]https://youtu.be/vdRDmy_tou4[/url]

Ok:smile:

Nice.

But man, didn't you find a larger font? And more red? :razz:
(it really hurt the eyes to read that!)

0[QUOTE=LaurV;576062]Nice.

But man, didn't you find a larger font? And more red? :razz:
(it really hurt the eyes to read that!)[/QUOTE]

Hahaha
For the red, I would have liked you to see it in green !. But presbyopic peoples are very rare !!
:le sourire:

Confused about the bolded part: "Your goal: Find an n such that there is a set of unwinnable numbers for [B]seven steps (i.e., the set is of size n-7)[/B]. In your answer, supply the number n and the elements of the unwinnable set." So are the amount of steps and the amount of spins both equal to 7? Or did they mean that there are 7 spins and q can be any value we find that results in at least 1 unwinnable set?

[QUOTE=Yusuf;576706]Confused about the bolded part: "Your goal: Find an n such that there is a set of unwinnable numbers for [B]seven steps (i.e., the set is of size n-7)[/B]. In your answer, supply the number n and the elements of the unwinnable set." So are the amount of steps and the amount of spins both equal to 7? Or did they mean that there are 7 spins and q can be any value we find that results in at least 1 unwinnable set?[/QUOTE]
Look at #2! That was my first comment.