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Ace2
Ace2
Joined: Oct 2, 2017
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Thanks for this post from:
miplet
June 8th, 2021 at 9:01:00 AM permalink
You should win a million dollars just for understanding the rules of the game
Itís all about making that GTA
ThatDonGuy
ThatDonGuy
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June 8th, 2021 at 2:31:05 PM permalink
Quote: Ace2

You should win a million dollars just for understanding the rules of the game


I think I can rephrase the problem:

There are n persons standing around a circle, numbered in order 1, 2, ..., n.
Starting with person 1, then going to 2, 3, and so on, count q persons, then remove that person from the circle.
Starting with the person after the one removed, count another q persons (in the same direction), then remove that person as well.
Stop when k people remain.
For all n < 9, for every value of k, every "ending condition" of k people still around the circle is possible - i.e. there is at least one value of q where you will end up with that set of people.
For n = 9 and k = 5, you cannot end with (1, 2, 5, 8, 9), (2, 3, 4, 5, 8), or (2, 5, 6, 7, 8), but you can end with every one of the other 123 sets of 5 people out of 9.
The problem: find a value of n such that at least one impossible ending condition exists for k = n - 7.
ThatDonGuy
ThatDonGuy
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June 9th, 2021 at 6:21:52 AM permalink
Quote: Gialmere

It's toughie Tuesday. Here's a puzzle from the brainiacs at IBM...

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.


I think I am on the right track, but I want to make sure I'm not missing something...is there a solution with n < 19? I am trying brute force, but my code claims that every set of (n - 7) with n < 19 can be formed after seven steps, and it's going to take quite a bit of time to check n = 19.
Gialmere
Gialmere
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June 9th, 2021 at 8:04:09 AM permalink
n > 19

There's also a bonus question for finding an unwinnable set which takes more than seven steps.
Have you tried 22 tonight? I said 22.
ThatDonGuy
ThatDonGuy
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Thanks for this post from:
Gialmere
June 9th, 2021 at 9:37:55 AM permalink
Quote: Gialmere

n > 19

There's also a bonus question for finding an unwinnable set which takes more than seven steps.


I found a problem with my code that was causing it to run much slower than it should.


n = 20 has 2 solutions:
1,2,3,4,5,6,7,8,11,14,15,16,17
4,5,6,7,10,13,14,15,16,17,18,19,20

As for the bonus question:

n = 12, k = 8:
1,2,3,4,5,7,9,11
1,2,3,4,6,8,10,11
1,2,5,6,7,8,11,12
1,3,4,5,6,8,9,11
1,3,5,7,8,9,10,11
2,3,4,5,6,8,10,12
2,3,5,7,9,10,11,12
2,4,5,7,8,9,10,12
2,4,6,8,9,10,11,12

n = 15, k = 11:
1,2,3,4,5,6,7,8,11,14,15
1,2,3,4,5,6,8,9,10,11,14
1,2,3,4,5,6,8,11,12,13,14
1,2,3,4,5,8,9,10,11,14,15
1,2,3,4,5,8,11,12,13,14,15
1,2,3,5,6,7,8,10,11,12,14
1,2,3,5,6,7,8,11,13,14,15
1,2,3,5,7,8,9,11,12,13,14
1,2,3,5,8,9,10,11,13,14,15
1,2,4,5,6,7,8,9,11,14,15
1,2,4,5,6,8,10,11,12,14,15
1,2,5,6,7,8,9,10,11,14,15
1,2,5,6,7,8,11,12,13,14,15
1,2,5,7,8,9,10,11,12,14,15
1,2,5,8,9,10,11,12,13,14,15
2,3,4,5,6,7,8,9,10,11,14
2,3,4,5,6,7,8,11,12,13,14
2,3,4,5,7,8,9,10,11,12,14
2,3,4,5,7,8,9,11,13,14,15
2,3,4,5,8,9,10,11,12,13,14
2,3,4,5,8,10,11,12,13,14,15
2,4,5,6,7,8,9,11,12,13,14
2,4,5,6,8,9,10,11,13,14,15
2,5,6,7,8,9,10,11,12,13,14
2,5,6,7,8,10,11,12,13,14,15

n = 15, k = 9:
3,4,5,6,8,10,11,12,13

n = 18, k = 14 has 54 solutions
n = 20, k = 14 has 236 solutions

Last edited by: ThatDonGuy on Jun 9, 2021
ThatDonGuy
ThatDonGuy
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June 9th, 2021 at 10:28:04 AM permalink
Okay, not exactly a math puzzle...

In a game of chess, after White's fifth move, h1 is empty. (h1 is where White's king-side rook begins.)
Black's fifth move is rook to h1, checkmate.
What were the first 9 moves of the game?
Last edited by: ThatDonGuy on Jun 9, 2021
gordonm888
Administrator
gordonm888
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June 9th, 2021 at 3:43:18 PM permalink
I have been really enjoying the posts in which ThatDonGuy argues with himself. Very entertaining.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
ThatDonGuy
ThatDonGuy
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June 9th, 2021 at 5:11:09 PM permalink
Quote: gordonm888

I have been really enjoying the posts in which ThatDonGuy argues with himself. Very entertaining.


You're lucky - you don't have to live with him 24/7
Gialmere
Gialmere
Joined: Nov 26, 2018
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June 9th, 2021 at 6:16:05 PM permalink
Quote: ThatDonGuy

I found a problem with my code that was causing it to run much slower than it should.


n = 20 has 2 solutions:
1,2,3,4,5,6,7,8,11,14,15,16,17
4,5,6,7,10,13,14,15,16,17,18,19,20

As for the bonus question:

n = 12, k = 8:
1,2,3,4,5,7,9,11
1,2,3,4,6,8,10,11
1,2,5,6,7,8,11,12
1,3,4,5,6,8,9,11
1,3,5,7,8,9,10,11
2,3,4,5,6,8,10,12
2,3,5,7,9,10,11,12
2,4,5,7,8,9,10,12
2,4,6,8,9,10,11,12

n = 15, k = 11:
1,2,3,4,5,6,7,8,11,14,15
1,2,3,4,5,6,8,9,10,11,14
1,2,3,4,5,6,8,11,12,13,14
1,2,3,4,5,8,9,10,11,14,15
1,2,3,4,5,8,11,12,13,14,15
1,2,3,5,6,7,8,10,11,12,14
1,2,3,5,6,7,8,11,13,14,15
1,2,3,5,7,8,9,11,12,13,14
1,2,3,5,8,9,10,11,13,14,15
1,2,4,5,6,7,8,9,11,14,15
1,2,4,5,6,8,10,11,12,14,15
1,2,5,6,7,8,9,10,11,14,15
1,2,5,6,7,8,11,12,13,14,15
1,2,5,7,8,9,10,11,12,14,15
1,2,5,8,9,10,11,12,13,14,15
2,3,4,5,6,7,8,9,10,11,14
2,3,4,5,6,7,8,11,12,13,14
2,3,4,5,7,8,9,10,11,12,14
2,3,4,5,7,8,9,11,13,14,15
2,3,4,5,8,9,10,11,12,13,14
2,3,4,5,8,10,11,12,13,14,15
2,4,5,6,7,8,9,11,12,13,14
2,4,5,6,8,9,10,11,13,14,15
2,5,6,7,8,9,10,11,12,13,14
2,5,6,7,8,10,11,12,13,14,15

n = 15, k = 9:
3,4,5,6,8,10,11,12,13

n = 18, k = 14 has 54 solutions
n = 20, k = 14 has 236 solutions


Correct!

Very good. (I liked the "bubble gum, bubble gum in a dish" analogy.)
---------------------------------------------------

Have you tried 22 tonight? I said 22.
Ace2
Ace2
Joined: Oct 2, 2017
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June 9th, 2021 at 7:20:32 PM permalink
Assuming an infinite standard deck of cards, you draw until you have all thirteen cards of any suit (diamonds, hearts, spades or clubs).

On average, how many draws will it take?
Itís all about making that GTA

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