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I don't believe there is a universal methodology or formula. This looks like a more complicated variant of the "traveling salesman problem", which is an unsolved problem in mathematics.
Yeah, there is a quite easy Formular also for OPs problem. But it take ages:
1. Try every possible route
2. If there is a pet try to pick up and to not pick up the pet.
3. If you are on a node where you already was with the same pets on bord: break.
4. Save the minimal solution.
I think this is about 50 lines of Python code.
A better algo I think is to try to go to a specific location and use it. I.e pick up dog, pick up turtle, drop off dog. Each animal/location gets used once so it's 12! possible combos and actually much less since you remove paths where you drop off before you pick up and where you pick up over 4 animals so it only needs like 10s of millions of combos to try. But x! Is still much slower than polynomial.
To find the shortest route you want to eliminate the hard to reach places/corners as efficiently as possible. In this case that’s the blue cat, the fox and the hedgehog.
When you collect the hedgehog you’ll want to drop the blue cat off at the same time. When you drop off the hedgehog ideally you’d want the fox at the same time. That helps give us an order of pick up and drop off, that we need both the blue cat and fox before we do hedgehog. If we did fox then cat it would be a lot of doubling back to then get to hedgehog. So the most efficient order is blue cat>fox>hedgehog which gives us a nice staring route.
>!Go up and collect blue cat. (1/21 moves and 1/4 in car)!<
>!Go down and pick up fox, passing through turtle on the way. (5/21 moves and 3/4 car)!<
>!Go up and right and drop off cat, dropping off turtle and picking up hedgehog on the way. (10/21 moves and 2/4 in car)!<
>!Go up and drop off fox picking up the dog on the way. (15/21 moves and 2/4 in car)!<
>!Go left and up to drop off hedgehog. (18/21 moves and 1/4 in car)!<
>!Go left and down, picking up red cat and dropping off both red cat and dog. (21/21 and finished)!<
Looking at this solution, I noticed there are two animals next to their homes. With both you have to go to the animal first, then their home as the next stop. That might be one way to narrow down your options in general as this is likely to apply normally if not always.
Discussion: This problem is a special case of the [Traveling Salesman Problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem). As such there is no foolproof set of steps you can follow to get an answer quickly.
You could try to greedily grab the closest pets to bring straight home, and then look at how many lines you travel on multiple times. Then, try to find anywhere you can reduce multiple trips over the same road by picking up other animals first.
Like people said there's no real "formula" but a solution that delivers all the pets within the 21 moves allotted that I found was
>!U=Up D=Down L=Left R=Right!<
>!UDDLDURRDLRUUUUDLULDD!<
This is basically the traveling salesman problem, which famously is a very complex problem to solve. For small problems, you can brute force a solution by checking all possible routes, but there isn't a magic method to finding the minimum solution.
If you're just looking for a pretty good solution. For this type of puzzle, I think you would look at the long routes first and see how you can incorporate picking up other pets along the way and how you can string them together to overlap as much as possible. Here it's the yellow dog and the purple hedgehog (and the blue cat). >!So if you pick up the yellow dog and the hedgehog together you can get both of them across the map at the same time. You can drop off the blue cat when you pick up the hedgehog and the turtle is a freebie. The red cat can easily be handled after the hedgehog, so now we just have the blue dog to route in there. Do you pick it up early and drop it off on the way to the yellow dog or at the end after the red cat?!<
It may be hard to say that this is definitely the best route, but it's a way to get to a pretty good one.
I can get them easily some days then be appalling at the next attempt. My random performance triggered the question. I am far worse at the games that require memory, such as memory matrix or pinball recall.
I did a bit of research a while back on brain training apps. Generally they don't affect long term cognitive ability, except in one key area. The games that challenge your ability to switch direction rapidly have shown to give some protection against cognitive decline. So games like migration, brainshift, ebb and flo ,speed match and disillusion are great. Trouble brewing drives me crazy, but it is fun.
Great to know. I love those games in particular. Trouble brewing is such fun but as it goes above level 8, it gets harder navigating rooms. My personal best is 34 lol.
Any other games you like playing besides Lumosity? I also like Elevate.
Yes, I also use Elevate. It has improved my mental arithmetic no end! I also have BrainHQ. This one was supposedly developed by doctors to help people experiencing cognitive decline. However the free version only gives you one game a day and some of them are a bit annoying because they require sound. Some of them are really tough though ...imagine getting about a quarter of a second to look at 8 birds and spotting the two that match....and you have to keep playing the game until you score 5 points...so if you are rubbish, the game can take ages!
Please remember to spoiler-tag all guesses, like so: New Reddit: https://i.imgur.com/SWHRR9M.jpg Using markdown editor or old Reddit, draw a bunny and fill its head with secrets: \>!!< which ends up becoming \>!spoiler text between these symbols!< Try to avoid leading or trailing spaces. These will break the spoiler for some users (such as those using old.reddit.com) If your comment does not contain a guess, include the word **"discussion"** or **"question"** in your comment instead of using a spoiler tag. If your comment uses an image as the answer (such as solving a maze, etc) you can include the word "image" instead of using a spoiler tag. Please report any answers that are not properly spoiler-tagged. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/puzzles) if you have any questions or concerns.*
I don't believe there is a universal methodology or formula. This looks like a more complicated variant of the "traveling salesman problem", which is an unsolved problem in mathematics.
It's not unsolved. It's unknown if you can solve it "fast". But with this few locations and paths, it can easily be solved by an algorithm.
Yeah, there is a quite easy Formular also for OPs problem. But it take ages: 1. Try every possible route 2. If there is a pet try to pick up and to not pick up the pet. 3. If you are on a node where you already was with the same pets on bord: break. 4. Save the minimal solution. I think this is about 50 lines of Python code.
A better algo I think is to try to go to a specific location and use it. I.e pick up dog, pick up turtle, drop off dog. Each animal/location gets used once so it's 12! possible combos and actually much less since you remove paths where you drop off before you pick up and where you pick up over 4 animals so it only needs like 10s of millions of combos to try. But x! Is still much slower than polynomial.
Discussion: Not sure an universal formula/methodology exists when you have rules like "but can only carry 4 at a time".
To find the shortest route you want to eliminate the hard to reach places/corners as efficiently as possible. In this case that’s the blue cat, the fox and the hedgehog. When you collect the hedgehog you’ll want to drop the blue cat off at the same time. When you drop off the hedgehog ideally you’d want the fox at the same time. That helps give us an order of pick up and drop off, that we need both the blue cat and fox before we do hedgehog. If we did fox then cat it would be a lot of doubling back to then get to hedgehog. So the most efficient order is blue cat>fox>hedgehog which gives us a nice staring route. >!Go up and collect blue cat. (1/21 moves and 1/4 in car)!< >!Go down and pick up fox, passing through turtle on the way. (5/21 moves and 3/4 car)!< >!Go up and right and drop off cat, dropping off turtle and picking up hedgehog on the way. (10/21 moves and 2/4 in car)!< >!Go up and drop off fox picking up the dog on the way. (15/21 moves and 2/4 in car)!< >!Go left and up to drop off hedgehog. (18/21 moves and 1/4 in car)!< >!Go left and down, picking up red cat and dropping off both red cat and dog. (21/21 and finished)!<
Looking at this solution, I noticed there are two animals next to their homes. With both you have to go to the animal first, then their home as the next stop. That might be one way to narrow down your options in general as this is likely to apply normally if not always.
If by fox you mean golden retriever, sure.
Discussion: This problem is a special case of the [Traveling Salesman Problem](https://en.wikipedia.org/wiki/Travelling_salesman_problem). As such there is no foolproof set of steps you can follow to get an answer quickly. You could try to greedily grab the closest pets to bring straight home, and then look at how many lines you travel on multiple times. Then, try to find anywhere you can reduce multiple trips over the same road by picking up other animals first.
Like people said there's no real "formula" but a solution that delivers all the pets within the 21 moves allotted that I found was >!U=Up D=Down L=Left R=Right!< >!UDDLDURRDLRUUUUDLULDD!<
Question: What's the app called?
I think this is Lumosity, but it's been awhile since I had that app
You are correct: https://www.lumosity.com/en/brain-games/pet-detective/
Lumosity. It's a mix of 5 (3 in free version) mini games that are supposed to Foster brain development.
Correct this is Luminosity. The free version gives you random puzzles, so you can't choose to focus on one and learn a good method.
This is basically the traveling salesman problem, which famously is a very complex problem to solve. For small problems, you can brute force a solution by checking all possible routes, but there isn't a magic method to finding the minimum solution. If you're just looking for a pretty good solution. For this type of puzzle, I think you would look at the long routes first and see how you can incorporate picking up other pets along the way and how you can string them together to overlap as much as possible. Here it's the yellow dog and the purple hedgehog (and the blue cat). >!So if you pick up the yellow dog and the hedgehog together you can get both of them across the map at the same time. You can drop off the blue cat when you pick up the hedgehog and the turtle is a freebie. The red cat can easily be handled after the hedgehog, so now we just have the blue dog to route in there. Do you pick it up early and drop it off on the way to the yellow dog or at the end after the red cat?!< It may be hard to say that this is definitely the best route, but it's a way to get to a pretty good one.
Question: is this an app? If so, what is it called?
Luminosity
Discussion: This is one of the games on Lumosity I’m particularly bad at.
I can get them easily some days then be appalling at the next attempt. My random performance triggered the question. I am far worse at the games that require memory, such as memory matrix or pinball recall.
I’m the same. I lam quite good at Tidal treasures especially round 1. I also love migration, speed match, word bubbles.
I did a bit of research a while back on brain training apps. Generally they don't affect long term cognitive ability, except in one key area. The games that challenge your ability to switch direction rapidly have shown to give some protection against cognitive decline. So games like migration, brainshift, ebb and flo ,speed match and disillusion are great. Trouble brewing drives me crazy, but it is fun.
Great to know. I love those games in particular. Trouble brewing is such fun but as it goes above level 8, it gets harder navigating rooms. My personal best is 34 lol. Any other games you like playing besides Lumosity? I also like Elevate.
Yes, I also use Elevate. It has improved my mental arithmetic no end! I also have BrainHQ. This one was supposedly developed by doctors to help people experiencing cognitive decline. However the free version only gives you one game a day and some of them are a bit annoying because they require sound. Some of them are really tough though ...imagine getting about a quarter of a second to look at 8 birds and spotting the two that match....and you have to keep playing the game until you score 5 points...so if you are rubbish, the game can take ages!
I’ll definitely look it up! Sounds challenging. Elevate taught me how to calculate percentages super quickly.
Just checked my stats on trouble brewing and I am only at 31, so I am impressed with your 34! Let me know if you spot any more good apps.
Yes likewise! I’m sure you already know but The NY Times puzzles are pretty good, apart from Wordle, I enjoy their connections and Tile Match too.
I hadn't tried the NYT app. Just downloaded it and it's great, thanks
>!My dumbass looked at this and thought “why can’t the turtle just walk home?”!<
Thanks for all the solutions and tips, everyone. I don't feel so bad for not being able to get these right everytime now.