mersenneforum.org April 2021
 Register FAQ Search Today's Posts Mark Forums Read

2021-04-05, 16:44   #12
Dieter

Oct 2017

2·59 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 2×59 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

1368 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

7616 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

10111102 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

2×47 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, 88 views) IBM Ponther This April 2021 unwinable sets Exemple 2.pdf (75.7 KB, 83 views)

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

 2021-04-13, 03:15 #18 Kebbaj     "Kebbaj Reda" May 2018 Casablanca, Morocco 2×47 Posts Ok
 2021-04-17, 15:58 #19 LaurV Romulan Interpreter     Jun 2011 Thailand 3×3,251 Posts Nice. But man, didn't you find a larger font? And more red? (it really hurt the eyes to read that!)
2021-04-18, 11:18   #20
Kebbaj

"Kebbaj Reda"
May 2018
Casablanca, Morocco

2×47 Posts

0
Quote:
 Originally Posted by LaurV Nice. But man, didn't you find a larger font? And more red? (it really hurt the eyes to read that!)
Hahaha
For the red, I would have liked you to see it in green !. But presbyopic peoples are very rare !!
:le sourire:

Last fiddled with by Kebbaj on 2021-04-18 at 11:23

 2021-04-24, 05:26 #21 Yusuf   Jan 2020 23 Posts Confused about the bolded part: "Your goal: Find an n such that there is a set of unwinnable numbers for seven steps (i.e., the set is of size n-7). 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? Last fiddled with by Yusuf on 2021-04-24 at 05:27
2021-04-24, 14:47   #22
Dieter

Oct 2017

2×59 Posts

Quote:
 Originally Posted by Yusuf Confused about the bolded part: "Your goal: Find an n such that there is a set of unwinnable numbers for seven steps (i.e., the set is of size n-7). 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?
Look at #2! That was my first comment.

 Similar Threads Thread Thread Starter Forum Replies Last Post gd_barnes Conjectures 'R Us 17 2021-09-19 18:00 tgan Puzzles 0 2021-02-28 13:30 tgan Puzzles 36 2021-02-09 21:29 Xyzzy Puzzles 11 2021-02-04 14:53 TommyJ Soap Box 2 2021-01-04 19:47

All times are UTC. The time now is 04:02.

Sat Sep 25 04:02:16 UTC 2021 up 63 days, 22:31, 0 users, load averages: 2.72, 2.17, 2.05