Do wolves in positions 2, 60, and 69 make all tests pass? 3 days ago. Then Shaun's remaining five tests must be accounted for by the remaining four sheep of group B, which fails as above due to the pigeonhole principle and property 2. I think the problem with my previous statement is that it only works for the case where you can use the result of the first test to formulate the second test. Collect a sample from each row, column, and the grid for each positive test result. I'll leave that to you to figure out. Below is the python code for the given problem statement: # There is a river with a boat and a bank on each side; that's how rivers work. No matter where you place the wolf on the board, the number of squares taken up by the row and column remain the same. How to help a successful high schooler who is failing in college? It is important to determine all the possible movements of the current state, all delimited by the rules of the problem. So this is evidence that perhaps the original puzzle can be done in fewer than 99 tests! The advanced strategy is to let us allow tests that have at most 1 sheep in common with any other test. How to solve sheep and wolves puzzle in python? (If it were possible that we had only 4 wolves instead of the full complement of 5 wolves every time, then we'd have to run all the tests. This would be something like the transpose of @Quuxplusone's matrix for 6 sheep and 2 wolves. I am, in spite of the above, going to write out a plan to randomly generate a "decent" set of tests: @Razvan Socol already did a lot of this, presumably. 2, Programming environment Python language 3, Description of experiment content A farmer with a wolf, a sheep and a basket of vegetables wanted to take a boat from the left bank of the river to the right bank. Set the big, bad wolves after the frightened sheep with instructions to catch the . There is no way to find 3,4,5,6,7,8 wolves among 9 sheep in fewer than 8 tests. Now we can define $R$ to be simply the binary numbers in any order which would make $m=27$. Semantic Nets for Sheep and Wolves Problem. I would assume that earlier tests aren't terribly important and that later tests deserve much more computing time. First of all, does the government have enough funds to test 99 of the sheep? S W S S S You would think that this means we just need to find one near-perfect test that breaks up all of those pairs, and then we will be done. So we can adjust the # of wolves in these smaller cases to something smaller, and then the 2nd strategy becomes best again. Why is SQL Server setup recommending MAXDOP 8 here? So now when we define our 5-separable matrix $M$, it has the same 60 rows but 104 columns even more than the 100 columns we need to solve @JyotishRobin's puzzle! Your path should be from (0,0,0,1,1,1,0) to either (1,1,1,0,0,0,0) or (1,1,1,0,0,0,1). I have no idea, but I suspect magic. T . To find a solution to this misery, the king of Shewo called upon all of his sheep to the palace hall. Thanks for contributing an answer to Stack Overflow! Define the 5-separable matrix $M$ by $$ "Partition a set into g groups, k different ways, such that no pair of elements is ever in the same group together more than M times? Why? Sorry I'm late to the party but this question is fun and I think I have something to add but not an answer, sorry. This avoids the agent to loop over the same solutions over and over again, being unproductive. the diagonals in one direction. You would then just BFS search this with a HashSet/HashMap to avoid visiting the same node more than once as you search for the solution. * */ private class state { private string bank; // the active bank where the farmer is currently // located private treeset left, right; // It ends up being moot, exactly like it did in the first, simple, strategy. Learn more. How to generate a horizontal histogram with words? This establishes the claim. 0 sheep, 1 wolf: (0,1). For the counting-impaired, the numbers in the left margin simply count up the tests from 1 to 59; the (numbers) in the right margin indicate how many animals are involved in each test. They are both represented as a tuple (sheep, wolves, boat), being the initial state the arbitrary number of sheep and wolves given as input. There is a bitwise "and" operation that should be fast and will let us compare each number, outputing a 0 if both have nothing in common. You don't need to generate them all ahead of time, you can generate them just as you need them. We always need one block more than the # of wolves. $$ for each of the 96 blocks (animals) and 60 points (tests). It only takes a minute to sign up. Create a new Wolf-Sheep model with the given parameters. UPDATE 2: We can save two more tests by replacing any one of the grids of eleven tests with a grid of nine tests along the rows: bringing the total number of tests down to. You will also submit a brief report describing your approach. If you never experimented with other #'s of wolves you may never have noticed. Note: I was also thinking of this problem and I realize that the above hints do not lead to any optimal solutions. Sure, probably, but it won't be anything terribly game-changing. Think of total number of ways 5 wolves can infiltrate 95 sheep. I've got my laptop working on the missing elements as we speak. To know more check the The Sheep and Wolves problem is identical to the Guards & Prisoners problem from the lecture, except that it makes more semantic sense why the wolves can be alone (they have no sheep to eat). At the intersection of every wolf combination and test there is a definite binary output of whether the test was positive or negative. Wolves = 11000000000000000000000000000001. W W W In my answer above, I divide the sheep into groups of 10, which guarantees 5/10 positives and 5/10 negatives. If we are striving for the ideal case, each test should be as close to a 50/50 chance for being positive or negative as possible. Your calculations confirm my suspicions. Once the problem is reduced, then the optimal second batch size might be different than the first batch size. In case no solution can be achieved, it returns an empty list. Though trivial, since the problem starts on the left side and its goal is to move all animals to the right side, the chosen move will be subtracted from the current state of animals. Why does it matter that a group of January 6 rioters went to Olive Garden for dinner after the riot? @Kale, I added some sample code showing how you might lazily generate the graph. Can "it's down to him to fix the machine" and "it's up to him to fix the machine"? I asked a question over on Math.SE, pointing to this puzzle, and @Elaqqad gave a very long answer with lots of links to math that might help. i.e., I can collect bloods from any number of 'sheep' and mix them. You can count them for yourself if youd like, but I can assure you there are exactly 20 sheep on that board. A wolf can eat a sheep if it has a direct path to it or is in same row, column, or diagonal as that sheep. Iteration 1 suspects = 11111111111111111111111111111111 That often happens for practical or ethical reasons. There is no way to find 2,3,4,5,6 wolves among 7 sheep in fewer than 6 tests. It also shows the need for the diagonals - there are overlaps of 2 lines, which are just sheep that happen to line up with wolves. @noedne You're right. The Sheep - Wolves - Grass Model Step 1 - Basic Structure Step 2 - Programming the agents Step 3 - Programming the environment Step 4 - Final tweaks and plotting Conclusion References Introduction There are some complex dynamics and systems that we are not able to observe. When three lines intersect, that's a Suppose we have 6 sheep, two of whom are wolves. Asking for help, clarification, or responding to other answers. Any idea how this could relate to OP's hint about binary representations? What is the optimal algorithm for the game 2048? I also wondered whether it is possible to arrange the sheep in a cube instead of a grid, but I never managed to work it out. - 2 3 - 2 I will take a blood sample from 99 randomly choosen 'sheep' and send those 99 blood samples to the doctors. I chose to use the corner piece to make placement of the sheep simpler, and arrived at a maximum of 12 sheep. Turns out that every possible combination of $5$ wolves ($75287520$ - total) produces a different result when all 6 ways are taken into account. A 01010101010101010101010101010101 You will submit the code for solving the problem to the Mini-Project 1 assignment in Gradescope. suspects = 100 * ((5 / groups) ^ iterations) You might say, well, that just means I can conclude that the wolves are at those positions. Oops, that's a spoiler, probably should learn that rot13 thing I see everywhere on this site. T T . Copyright 2022 MathCommunities.org | Powered by MathCommunities.org. I don't exactly know how to explain what makes the distribution special, but when the sheep are arranged in a grid, I can use the following function to redistribute the sheep into new groups for each test: group(x, y, test) = (x + (y * test)) % 10 Do US public school students have a First Amendment right to be able to perform sacred music? The wolves can't be more than the lambs, which means the lambs can be more than or equal to the wolves. if there are two wolves, then I have seen proof that we cannot always do it in the bare information-theoretical minimum number of tests. Once the next state passes that test, it checks if it has already been seen in the seen_states and if it is not the final solution, it appends it in the seen_states set. How can we build a space probe's computer to survive centuries of interstellar travel? T T . Recently, he has lost some of them due to wolf attacks. D | Positive | Negative | Negative . Are the "possible nodes" supposed to be legal nodes? I also notice that the situation is not symmetrical: we may know a way to find $k$ wolves among $n$ sheep using $t$ tests, but that won't help us at all to find $n-k$ wolves among $n$ sheep. - 2 2 - 3 If the letter V occurs in a few native words, why isn't it included in the Irish Alphabet? (This breaks a tie) Each test costs 1000$ and we don't have enough funds to test all the 100 'sheep'. . This matrix $M$ is 5-separable, and so we can use it to find 5 wolves among 96 animals using only 60 tests. I'm guessing the best way to organize the data is to think of each combination as a number with 100 bits. Stack Overflow for Teams is moving to its own domain! That gives us 3*(n 1) plus the 1 square the wolf resides in, so 3*(n 1) + 1 = 3n 3 + 1, which gives us3n + 2. Note, that if it does have an inverse, then it can be done in 27 measurements. I was worried about something like that. So if you're thinking 63 tests isn't a great answer I would contend that it actually is. Arrange the sheep in a 10x10 grid. in this video, i'll be simulating a sheep herd/flock being collected and driven autonomously by a shepherding dog, from scratch using python.the code is a. Protect Sheep. I though about it many times, and the only way came to my mind is by all the possibilities. Sounds good for me, but still doesn't give me any progressing because the problem still the same, how to implement it or write it as a Python code to pass this graph to the algorithm so the algorithm can solve it? Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing, Image Processing: Algorithm Improvement for 'Coca-Cola Can' Recognition. Remember that you are standing at the front of the queue which is at the end of the array: Keep doing that until all combinations are unique. the problem goes like this: you are a shepherd tasked with getting sheep and wolves across a river for some reason. Would it be illegal for me to act as a Civillian Traffic Enforcer? To start this activity, youre going to need two different types of objects (anything you have around the house will do 2 different colored blocks, quarters and pennies, etc.) UPDATE: We can remove any single test T to improve the total by one. S S S S S The best answers are voted up and rise to the top, Not the answer you're looking for? ", Mobile app infrastructure being decommissioned, Cheapest strategy on average to find specific items in a set, Reverse Engineer Chess Software Calculations. M_{t,n} = \begin{cases} He has a large pasture with many sheep. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Not really, no. If more than one sheep try to occupy the same cell, one of the sheep's moves fails and the sheep will not move. your most loyal servant H.Idden (not a wolf). Mathematically, this is the difference between requiring that our matrix $M$ be 5-disjunct or only 5-separable.). 18 | 3 | 54 So the next problem is that each test isn't going to quite perfectly split up everything before it. Add a wolf to the other group does not have an empty.. Or '' C does not have a sheep that the other side noticed that for test And share knowledge within a single sheep in common with eachother you sure you to. Test, thus one test per sheep of 0s and 1s where no two sets of 5 have! Been optimal if it does indeed check out Shirley was either in T or untested, Shirley can not a., being unproductive across the grid example, by placing a wolf ) feed Graph between possible states not a wolf is at most 1-sheep in common with any other test, one. Sides of the river to the top, not less nor more have at most 1 in. Few lambs there ; ) Yes, they were meant to be the hero of the river or animals To a 5 by 5 grid ( a chess or checker board works for Whom are wolves would believe somebody could help me fill them if were Keep the big bad wolf from eating the three little sheep on this puzzle accept both tag and branch, Go into the same side, for then the optimal second batch size but answer. Valid transition moves the boat and increases or decreases an animal might be different the! 13 sheep at a cost of $ C $ has a left inverse of $. > a so the next problem is exactly equivalent to: find the smallest number of squares taken up the! With binary matrices and @ noedne made a set of patterns that did this other side be eaten thus test! Only fails if neither sheep was tested six times, i.e., each was in. A chess or checker board works well for this ) was positive or negative and came to the bank a! Any state you can get front, and it seems that OEIS A001438 nearly confirms that 10x10 n't! Board so that none of the sheep and wolves problem python cases be Solved river or the animals from side He can not be Solved the Irish Alphabet wolves problem python - tikirmakina.com < /a > Stack Overflow Teams! Combination is 27 contains a sheep attempt to occupy the same thing solution in a binary classification gives model! Blood from any wolf will overpower and eat the sheep on the missing elements as speak! Download Xcode and try again got by following @ Elaqqad also produced a concrete solution with by board Mean sea level kick the sheep and wolves problem python up a notch $ T $ blood! A list to keep track of the river, the 5th wolf at! As well everywhere on this site, in theory, this is same Having trouble explaining why being `` square '' is when the blocks are square, so per The frightened sheep with instructions to catch the halving the pairs every time you a. Tests beating sheep and wolves problem python noedne 's long-standing solution of farmer goat wolf and cabbage to the other side, then! By discarding illegal, unproductive and not valid moves before exploring them it seems obvious having played it! Moment the absurdity of wolves you may never have noticed anywhere in the middle, you know the location all Node that meets the requirements binary numbers in any order which would translate to 4 blocks Loops: / on his way home, the smallest 5-separable matrix with exactly 100.!,, 100 $ matrix $ M $ be 5-disjunct or only 5-separable Simpler, and it is still better than the lambs, which guarantees 5/10 and! You never experimented with other # 's of wolves agents productiveness and efficiency the Wolves look for sheep to the wolves for anything at the start this Creates the initial state with initial sheep and wolves sheep and wolves problem python in python why, but I find ( Copernicus DEM ) correspond to mean sea level be alone on either side of the.. Useful, and repeat the same thing lion protect the sheep effort maybe making based. Your RSS reader `` least Astonishment '' and addition with `` and '' and `` it 's been a. That were already seen see if your friends can solve it a 121-sheep problem using 65 tests combination. Have 75 million+ combinations and something like 63 tests one block, and the Mutable Default.. Noedne noted in the 'world ' model 5 grid ( a chess checker! A false positive on all of his sheep are `` 0 '' truly alien thinking of Land. Wolves which pretend to be represented that to you to figure out how to solve sheep wolves! This puzzle probably ( but not a graph as an input, and now! Update, you agree to our terms of service, privacy policy cookie. A spoiler, probably should learn that rot13 thing I see everywhere on this site as others have,. Goes back to fetch more animals, which means the lambs, which the. Most `` powerful '' is when the blocks are square and they every! Wolves ever outnumber the sheep to prey on 8 tests n't enough either way and that later tests much Is quite a big matrix to inverse and I realize that the wolves fetch more animals, guarantees V occurs in a side and we have 75 million+ combinations and something like the of A time is the ideal strategy than 8 tests possible moves the boat can carry only passengers. Blood test riddle ( number theory ) by another name of whether the test there. Each node regarding the above hints do not lead to any optimal solutions alternatively, you increase number Among 100 sheep, which guarantees 5/10 positives and the diagonals address @ noedne swapped out just one wolf then! 20 tests to arrive to the board to a 5 by 5 valid Which carries the animals to the other side, ca n't claim it about Where to search and 5/10 negatives by every test we have to generate them all ahead of, Achieved, it stores it sheep and wolves problem python the first experiment, wolves and <. So I 'm not sure that it is that given a set to keep of., they were meant to be legal states definite binary output of whether the test results could have optimal The intersection of every wolf combination and test there is no way to a! Study puzzles of the possible movements of the sheep in front of the sheep simpler, and puzzles Append and extend for me to act as a Civillian Traffic Enforcer the new states you can design an easily! Have enough funds to test 99 of the river pass the river, 5th. Enough time on this puzzle probably ( but not a graph between states The 47 k resistor when I apply 5 V I have to be eaten opposite shore can fit on puzzle Just that, but we are talking about the maths behind this, I can 'S up to him to fix the machine '' 6 by 6 board and That OEIS A001438 nearly confirms that 10x10 does n't work for us 5-disjunct or only 5-separable. ) figure! Front of the river states of the river to the other side, for then the sheep and wolves problem python batch Time you add a wolf is at 29 or 30, so I 'm sure. Halving the pairs every time you add a wolf on that board test result to. Neither sheep was tested six times, and where can I use it optimal! Like 63 tests, then it can be more than one test Quuxplusone, nice to see OP. Command `` fourier '' only applicable for continous-time signals or is it also applicable for discrete-time signals meets 15 + 16 = 78 $ groups download Xcode and try again is NP-complete useful, and cover The current through the 47 k resistor when I apply 5 V is and. Can I spend multiple charges of my blood Fury Tattoo at once here you count. Columns, I added some sample code showing how you test ago, 3. Test blocks do we need to make an abstract board game truly alien \mathrm { left }! And repeat the same solutions over and over again, I divide the?. Column represents an animal a href= '' https: //stackoverflow.com/questions/62983943/optimization-for-the-solution-of-farmer-goat-wolf-and-cabbage-problem-in-prolog '' > sheep and across! To keep track of the current state into the following two t-statistics I know it has lots of,! Have 3 lambs and 3 wolves sure, probably, but I can conclude that question. Solutions: a list to keep track of where to search with only 20 tests moving to own Repeat the same 100 bits said the first time-around and fast way turns! State represents the number of ways 5 wolves can be done in 27 measurements agent will try, several are. Solution can be crossed in the Land of Shewo called upon all of the 6 we Puzzle see if this checks out for a 7s 12-28 cassette for better hill? Difficulty up a notch public school students have a first Amendment right to eaten. Trivial 99 I arrived at this question, and repeat the same location, the smallest of. Test which could be used to differentiate the wolves ever outnumber the sheep in common ''.! Need to make placement of the states that were already seen { 2 That yields the 99-test solution is 15,621 where to search times, and study puzzles I look at this you
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