Easy math puzzles
Poll
 | 20 votes (46.51%) | ||
| | 14 votes (32.55%) | ||
| | 6 votes (13.95%) | ||
| | 2 votes (4.65%) | ||
| | 12 votes (27.9%) | ||
| | 3 votes (6.97%) | ||
| | 6 votes (13.95%) | ||
| | 5 votes (11.62%) | ||
| | 12 votes (27.9%) | ||
| | 9 votes (20.93%) |
43 members have voted
June 8th, 2021 at 9:01:00 AM
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You should win a million dollars just for understanding the rules of the game
It’s all about making that GTA
June 8th, 2021 at 2:31:05 PM
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Quote: Ace2You 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.
June 9th, 2021 at 6:21:52 AM
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Quote: GialmereIt'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.
June 9th, 2021 at 8:04:09 AM
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n > 19
There's also a bonus question for finding an unwinnable set which takes more than seven steps.
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.
June 9th, 2021 at 9:37:55 AM
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Quote: Gialmeren > 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
June 9th, 2021 at 10:28:04 AM
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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?
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
June 9th, 2021 at 3:43:18 PM
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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.
June 9th, 2021 at 5:11:09 PM
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Quote: gordonm888I 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
June 9th, 2021 at 6:16:05 PM
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Quote: ThatDonGuyI 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.)
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Have you tried 22 tonight? I said 22.
June 9th, 2021 at 7:20:32 PM
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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?
On average, how many draws will it take?
It’s all about making that GTA
