A cheesy puzzle!? Definitely not! - 4 Parts that drive you crazy!
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- Опубліковано 5 жов 2017
- Alles Käse! - Four pieces of cheese that need to be packed in the wooden frame. Well, the last part just doesn't want to get in! Thanks to the precise cut, this puzzle is a great challenge! Worship the laser cutters!
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“Start with the corner pieces”, they say.
And continue with the corner piece then finish with the corner piece
Much easier than the Giraffe Puzzle
Zigmaker 😂😂😂
Every puzzle is easier than the Giraffe Puzzle
I dont know. The giraffe puzzle was kinda hard.
@alex z
That's it!
Zigmaker Meh. I’ll take water from the Nile over the giraffe puzzle any day 😆
It's kinda disappointing to see that the pieces (and 'cheese' holes) don't fit exactly. Of course that's not your fault, it's just unsatisfying to watch.
If you would have to align the holes the solution would be too easy.
There would be not too many possibilities.
It probably triggered someone's OCD if they have it
The corners not being right angles is annoying too. It fits, but it just looks unsatisfying and sloppy.
Oh, okay. Thanks for telling (:
ok
Thats not really what ocd is lol
First of all, we have 2 ways to arrange each piece. top side up, or bottom side up and that with 4 orientations each. so that's 8^2 for 2 pieces and 8^3 for 3 pieces. Why 2,3 and not 4 due to only 1 right angle, you'll see later. Now when I look at this puzzle, i am seeing that at least 2 pieces, might they be in any orientation, fit together in this. Thus the 8 orientations of a piece. Now choosing 2 pieces from a set of 4 is 4!/2!2!=6 ways. Arranging them in any of four spots is 4x3=12. So total ways of trying in a *best case scenario* in which you realize after putting just 2 pieces in 8^2 ways that it is wrong or right, is *(8^2)(6)(12)=4608* !! viola!! Although if you want, you could divide by 4 for rotational symmetry purpose = 1152 possibilities. if you consider the *worst case scenario* , in which you put at least 3 pieces before realizing its wrong then it will be *(8^3)[C(4,3)](3!)=(8^3)(4)(6)=12288* . consider rotational symmetry and 12288/4 =3072 ways!! Done *(I am excellent with combinatorics and I have tried the puzzle fitting in 2 or 3 ways myself. Hence my conclusion!!)* Also if you do 1 try in 10 seconds, it'll probably take you 7-8 hours for getting solution with worst luck possible. Thanks for not tl;dr ing this
Why would you try different ways of choosing the first 2 pieces? You could just start with the same 2 pieces each time. And when you mention dividing by 4 for rotational symmetry, you are forgetting about flipping. So I think the time estimate should be more like 35-40 minutes.
Actually, I also think 10 seconds per attempt is unreasonably long. If you try all possible positions for the third piece for a given arrangement of the first 2 pieces, it doesn't take 10 seconds to try each position of the third piece. So I think that with a very methodical search for the solution, it could be done in less time than it took Mr. Puzzle.
If you consider each piece to have 4 different ways to arrange it on each face and each piece has 4 possible corners to be put in. Then the very first piece you place has (4)(2)(4) different possibilities. After you place the first one you can arrange the rest of the pieces in 3! different ways, but that's without rotating or flipping so again we have to multiply each piece by 4 and by 2. So (4)(2)(4)(3!)(4^3)(2^3) = different combinations. I am aware this number would be correct only if all the pieces were to physically fit in every given order. And I also don't know how to simplify for rotational symmetry but I believe this is closer to the real approximation.
Additya Si, if at the worst scenario you realize that after 3 pieces the 4th would not fit, surely you wouldn't have to try to test all of the 8 possible settings for the last part, but you mustn't forget about them, the fourth piece has to be included in the calculation,
otherwise you had to withdraw all other impossible solutions, that's not the name of the game.
And you've forgotten about flipping the whole puzzle upside down. Yes, I nearly forgt about rotation symmetry
My calculation for this is quite nearly the same as yours, assuming the inner frame is a perfect square, rotation and flipping symmetry can be crossed out, it's
((4×2)^4 × 4!) ÷ (2×4) = 12288
the number of permutations you've calculated earlier in your posting.
If it's an assymetrical frame, it'll be just 8^4×4! = 98304
Additya Si I
Y'all boys out here wildin
I swear I would be the only fool to try and match up the holes. Fantastic video by the way! Always puts a smile on my face when I see your notifications pop up.
Glad I am not the only one!! :)
Wrong approach this time! :P
Ya I realized really soon that was not going to slide! Right when I got your notification my cat started laying on my chest. It is difficult to type this response .
Don't be silly, they aren't from the same cheese! :P
Ik I was thinking the same thing
I just double checked the official solution. You can download it by using the link in the description. The both parts on the top are the same. The lower parts are oriented in a different way. Well, I think there exist at least two solutions that work! By the way, the holes do not have to be aligned! :)
Mr.Puzzle thanks for the clarification. I’d have bet good money that the holes were a clue, just shows why I’m not up to your level of puzzle solving :) (love your channel btw) 😊
There are 98,304 possible combinations.
4 choices for the first piece used
3 for the second
2 for the third
And only 1 for the last
Each piece has 8 orientations
So 32 x 24 x 16 x 8 = 98,304
2 solutions
Each solution can be rotated 4 different ways and another 4 for the flipped versions
Technically there are 16 solutions for math’s sake
For the number of orientations without using identical, but flipped solutions, take the 8 out of the original equation. 8 being the number of ways you can use the same solution.
That equals 12,288 unique possibilities with 2 possible solutions.
It’s still a lot though lol
what in the actual fuck
I write this with love. It would be better to say "By the way, the holes do not have to be aligned!" Love your videos!
@MrCinnamonWhale: Your calculation is correct, but it seems rather error prone to mix orientation and permutation.
Each piece has 8 orientations -> 8^4
The pieces have 4! permutations
Total number: 4! * 8^4
Now we can ask, whether the frame is a perfect square. In that case, we can always group 8 of those configurations into a class of equivalent cofigurations. This reduces the number of "distinct" configurations by a factor of 8.
Also, you did not consider the center of the square. For some configurations - especially the shown solution - we can get a case, where two diagonally opposite pieces touch on an edge (the horizontal one in the shown solution). By rotating both pieces slightly we could make them touch with their vertical edges. This should be counted as two distinct configurations. However, I suppose this doesn't occur on all configurations and therefore can't be computed by combinatorics, but instead requires exact knowledge of the pieces' geometry.
My OCD does not like this puzzle.
Set Qesu me toooo
Not everybody has ocd, please stop using the term incorrectly
I _don't_ have OCD, and the pieces not fitting in the corners gets my hackles up...
Its lasercutted
Well I do so fuck off.
I just absolutely watch these because listening to him is just ridiculously mesmerizing. Im not one for puzzles per say, but I love watching him dive into solutions and speaking. all he would have to do is talk and I would watch his videos.
12288. 4! = 24 ways of putting the 4 pieces in corners; each piece has 4 rotations x 2 sides (i.e. 4! x 8 x 8 x 8 x 8 = 98304); but ÷ 8 because the frame can be any way up, and is isomorphic under reflection. That's excluding the small rotations needed to solve it, which are continuous, and so make it infinite.
The frame is symmetrical, you don't need the "4". BTW, 4x8x8x8x8 is not equal to 98304. rip
The frame may be isomorphic under reflection, but technically that doesnt change the fact that each orientation of the solution is still a different solution. Technically all the pieces fit and are in different positions relative to you (the viewer) making 8 different solutions. So there are 98,304 set possibilities
The Crafted Warriors that is not true its 65536
@Akai Nishin: Congrats - the most elegant and correct solution. An other way(without dividing by 8) is to assume a specific piece in a specific corner with a specific side up. (3! x 4 x 8 x 8 x 8)
In true, there are many mathematicians here. With me there are n + 1. 🙂🙂🙂
Interesting solution - never expected to fit the pieces with more than 90 degrees angle on the corners. :)
A second solution would be this one: flip every piece upside down and put them inside mirroring the current solution.
You are right!!!!
To me this is the same solution, though :)
You're making the assumption that the empty space is a perfect square. Without having the actual game in front of you, you can't be sure if the quadrilateral might be slightly off from a square, just enough to prevent rotation/mirroring.
You're right, I never thought about that it isn't a perfect square...
This puzzle is so much more simple than people keep saying... yes it has 4 corners, but that doesn't matter because it's a square, the solution will fit regardless of orientation, or even if you flip it upside down or backwards. You have 8 orientations per piece, and 3 possible patterns (red diagonal from white-orange diagonal from brown, etc). There's 12288 combinations if you don't count rotating the puzzle as a different combination, and most of them can be instantly thrown out if the first two pieces don't fit.
0:32 "And the target of the puzzle is- we need to fit all of these four parts inside of the frames, getting flush with the height of the frame." *Sees solution* wtf
What's wrong with the solution?
Willem Maas "Flush"
I hear ya. The holes didn't even match up. That surely can't be the solution.
@@WeavesWorldOFFICIAL it isn't the right solution. However, even on the official solution, the holes still don't match up but the edges of the pieces are flush and the pieces are all tilted at the same angle
@@WeavesWorldOFFICIAL Makimg the holes line up in such a puzzle will make it a lot easier. Those holes were probably never intended to match
I love watching your videos before bed. They’re so relaxing!
the total combinations are 863,040.
what I did is like one piece has 2 faces and each face can have 4 orientations , that means each face is equivalent to 8 unique figures, and we have 4 of them, that counts to be 32, now we need to select any four of these 32 to get in the box at a time i.e 32C4 and u can arrange them in themselves too, i.e 32C4*4!, which finally gives the result 863,040
IceCube Gaming quick maths
That is incorrect. You are counting impossible ways of placing them due to the fact that WLOG let's consider the first 8 elements the figures of the first piece the 2nd 8 the ones of the second.... the forth. You are including possibilities of selecting more than one of the first, and/or second and/or third and/or fourth group. So that is a lot more than it should be. Correct way would be to pick one of all 32 figures - (32 1) = 32. For the second one we can pick of only 3 remaining groups, i.e. 24 figues - (24 1) = 24 , then (16 1)=16 and (8 1) =8. Now due to the multiplication principle we multiply the results and get 32*24*16*8 = 98304.
You should multiply by 4! not just 4. Imagine one placement of pieces. Multiplying by 4 is like saying "Hey I can rotate these pieces!" you let the pieces have the same "partners" on their clockwise and counter-clockwise sides (or you could just call it left and right sides). However imagine this. In our original position I switch the upper right one with the lower right one. Now I get a new placement that I did not account for. The multiplication by 4! is something standard for combinatorics as you can imagine each of the places as let's say boxes in a row. If I now ask the question, "In how many ways could I arrange the pieces in the different boxes?" the answer is the rather obvious permutation of 4 elements(or whatever the proper wording would be in English), which is 4!.
Nyet! Get the hammer!!
Naaahhhhh, no hammers anymore! :D
Anon Ymous Lol, Russian.
A real Russian would: 1) Get the vodka, 2) Use the interfering corners as Zakuska, 3) Eat the rest of the puzzle, 4) Get asleep at the table with the Giraffe puzzle. Unsolved, naturally.
My puzzle from Puzzlemaster arrived at the weekend and I am delighted with it. The quality of its manufacture cannot be over- emphasised - it really is superb. I have not solved it yet and of course I have not watched the portion of this video after the spoiler break! It's a great little finger fidget that's rather more constructive than most and I really love that! Thank you Mr Puzzle!
Laser-cut wood.....
FINALLY!
😂😂
Flying Flurrox I also watch William Osman and Peter Sripol
RoastymyToasty yeah great he learned it, but it looks more like plastic ;)
Actually doesn't Wintergarten have some lazer cut wood on their MMX?
Your videos help my anxiety at night a lot. Thank you so much!
Each piece has 8 orientations (4 rotations one way up, 4 the other), and there are 4!=24 ways of positioning the pieces, which gives 98304 arrangements of the pieces. However, rotating an entire arrangement or flipping it yields an identical arrangement, so we counted each arrangement 8 times, so there are 12288 arrangements to check. These could be checked by fixing the orientation (but not position) of a particular piece, and trying all 8x8x8x24 combinations of orientations of the three other pieces, and positions of the 4 pieces.
You should have made it so one of the corners went into the cheese hole on another piece!
This would limit the variants a lot.
that would make me cringe so hard
This is what I was expecting.
Do you notice where the side holes are ? Middle area, which require the next piece to be in X instead of + (juxtaposed)
Antichrist, not okay man haha
Can you make a video showing the official solution? It looks cleaner in the PDF.
ITS YA BOI MR PUZZLE,BACK WITH ANOTHER VIDEO
Yeah!
I like that you called them by their name Tangram. My father gave me one about 45 years ago made out of Titanium, and the eight pieces could also be turned forward or backward. It is still my treasured keepsake. He died three years ago, but knew of my curiosity as a young man. I like your videos - Thanks !
I just purchased this puzzle and I actually found 3 different solutions that work😁
For the single piece it's 32 different position.....the second piece is 24... The third one is 16.... The forth is 8.... This gives us about 32*24*16*8 which equals 98304 combination
LMAO 32... pghhgahahahaha I'm dead
Why dead?
Kimo Saber cuz its wrong
L Jackson.... It's 100 % right
yes, it's right!
I think the comment section has many mathematicians
I know, right?
Except for the one comment that I saw talking about the Hammer that solves the puzzle 99.99%. I think he/she is not a mathematician but a Carpenter
We need big syaq
Abhijith S
They watch Rick and Morty
LOOOL .. That's right .. Master Carpenter here .. WE spend our time riddling out blueprints and going on Easter Egg Hunts all the time .. Puzzles are part of our job and the solution many times is just smashing it together !! Problem solved !!
These kind of puzzles are why I am a contractor; with many wood working tools. It is amazing how easy these puzzles get, when introduced to my chop saw.
Tyg Rahof it's also amazing how easily you can rob yourself of the thrill of overcoming a challenge.
512 variations (4⁴ for four pieces being able to be put into 4 different positions on one side, then you multiply that by 2,for the pieces having two sides.)
What type of cheese do you think it is? I’m going with Swiss. If you have different opinions or think that each piece is a different cheese, please let me know.
I’m no mathematician, but I think there is more than one solution.
Well at least 8
i love your videos so much i hope you make many more!
A quick 10 second calculation led me to 98,304 combinations:
First piece has 4 locations, 4 orientations, and 2 flips.
Second piece would have 3 locations, 4 orientations, 2 flips.
Third piece has 2 locations, 4 orientations, 2 flips.
Last piece has 1 location, 4 orientations, 2 flips.
Simply multiply all them together, right? I'm pretty sure math is good here.
2*4 for the first part (the frame is rotationally symmetrical) the second can be in 1 of the 3 corners left: 2*4*3 the next one in one of the 2 left: 2*4*2 and the last one has to go in the last corner: 2*4. Calculating the product of this gives us 24576 combinations.
(You could argue that the first can be in one of the four corners to give us 98304 combinations)
Rikkie Gieler whaattt !!😂😂😂 you're going mathematical
I don't think any _exact_ calculation can be made for this puzzle, given the fact (which I suspected from the beginning) that it's solution doesn't involve exact alignments and frame space-filling.
Dries Van heeswijk what do you mean?
4 different rotations of the shape and 2 sides. 2*4 = 8. There are 4 pieces which mean you have to do 8*8*8*8 = 4096 different possibilities.
I have no idea what you are calculating but if you are calculating all the different arrangements, I'm not sure it is correct.
[EDIT] I am no maths genius. If I am wrong don't take my comment as an insult.
@Nathan, That's the number i came up with as well.
When he said "The pieces are made of..." I would have loved to hear "cheese"
Looks like a great puzzle!
Wow, thanks youtube for bringing me to this channel. You're really cool Mr. Puzzle!
Each piece has 8 ways to fit, 4 rotations on the front and 4 on the back. The first piece has 4 places to go. 8*4. The second piece has the same 8 rotations, but now it only has 3 spaces to choose from. 8*3. The third piece has 8 orientations as well, but now only 2 spaces to fit in. 8*2. And finally, the last piece still has 8 possibilities, but only 1 space to go into. 8*1, or just 8. You find yourself with 8((8*4)(8*3)(8*2)), or 8((32)(24)(16)). This leaves you with the final result of 98,304 possibilities. (Trust me, I’m good with math)
@The Crafted Warriors: Why do you write "Trust me, I’m good with math" - what purpose does it have - other than make you look stupid. Your final solution is the same under rotation and flipping, so you need to divide your answer by 8. - giving 12288.
I said (trust me) so that all the frickin 5th graders doing 4x4x4x4 can look and understand that I know what I’m talking about and will be more inclined to trust my answer. Also, on a side note, I get what you’re saying with the reply, but even though you may just be rotating one of the possibilities 90 degrees to the right, all the pieces are in a different position in relation to the viewer, so by extension, it is technically a whole different orientation all together. So im sticking with 98,304 :/
You are correct. -but counting in that way means that there are 8 solutions for each unique way to solve(show me one and I can easily show you seven others).
Yup.
"the crafted warriors"
"fricking"
":/"
"trust me im good with math"
Peal the stickers off and stick em back on in the right place
Seth Likes Things Or break the corners out of the frame and reassemble the puzzle.
Seth Likes Things this ain't a rubiks cube
but when people do that the stickers get all gross and messy Ewwww D:
@@4jspa286 ahhh rubiks cheese
@@trishabayley6669 lmao
This puzzle would have drove me nuts because I would have expected a perfectly fit puzzle with matching pieces and holes. I wouldn't ever had settled for a soultion like this.
how could this not be called "who moved my cheese"?
Are you sure that's the right solution? the pieces seem like they fit on accident
Sten Mashups I think that's the point, it's what makes the puzzle more difficult, you wouldn't think to put the pieces in that way.
Sten Mashups id have thought the orientation of the holes was part of the puzzle. I think there must be a more elegant solution but I can’t deny the one shown does work! :)
Puzzles like this where you have to force a piece through a choke point are pretty unsatisfying. You can see in the final shot of the assembled puzzle some of the piece corners are starting to chip out from the rough handling required to coax them into position.
Blargo
They are satisfying to me because they represent what is best in a _perplexing_ puzzle, they defeat the mind's propensity for finding solutions based on assumptions of platonically ideal elements that need nothing more extracting the optimum from permutations of rotations by some explicit or intuitive application of algorithms.
No, the pieces have to be actually handled and played with and fiddled with. You cannot eyeball the solution. Unfortunately, it means the video is also useless until you actually _do_ look at the solution, unless you have the puzzle yourself.
Until he got to the end, I was SURE the solution was going to require some corner of a piece going in the indentation of a cheese hole.
It looked huge till you put your hands around it. Lol
I love how every doesnt realize alles käse directly translates to everything cheese in english i love the vids keep up the amazing work
to be true I just love see you solving it.
not OCD friendly puzzle indeed.
it grind you so hard
Obsessive-compulsive disorder is a DISORDER, not a quirky personality trait or a slight annoyance, not an adjective or perfectionism. It can severely affect someone's life and it's not something you should use to describe being annoyed because puzzle pieces don't fit in the corners perfectly. Take mental health and obsessive-compulsive disorder seriously, for the people who actually were diagnosed with the illness.
There's at least 2 variations
Michael Morris True mathematician right here
If the setting is actually a square, there are at least 8 solutions.
satisfying video as always :)
Hell yea, my boi Mr. Puzzle, back at it again
This isnt club penguin
Nothing is club penguin anymore
Mehr deutsch kann man kaum englisch sprechen😂 fire ich
DasIstKeinName das macht keinen sinn
DasIstKeinName lern Deutsch
Muss man auch erst mal schaffen! :P
Watch “The Post Apocalypse Inventor“ Videos und behaupte das nochmal
Lol
It's clear those pieces have to go in corners, and there are clearly 8 solutions, so the first piece can go in any corner on either side. It does have to be rotated the right way though. So each solution is 1 of 4*24*16*8=512*24=2048+10240=12288 "reasonable" configurations that have the same upper left corner on the same side. Multiply by 8 to get the total number of "reasonable" configurations (including all 8 solutions).
If my logic is correct: each piece has 8 possible orientations (4 edges * 2 sides). There are 4 total pieces, which means you can have 8^4 = 4096 sets of orientations for a given order of pieces, of which there are 4! = 24 permutations of unique orderings, resulting in 4096 orientation combinations per permutation * 24 permutations = 98304 possible outcomes
4 rotations, on two side orientations, in four different corners, for all four pieces that's 128 possible variations, many of which you will probably repeat, as they aren't exactly the easiest to keep track of. Any other factors I missed? Let me know and I'll update and edit.
can't there be more than 4 rotations?
You can't have any one piece in the same position. So even though there are four corners, it would be impossible to put more than one piece in a corner. You need to use combinatorics to calculate the answer.
Brian Halphin I
Ok so you can always fit at least 3 and there's only one combination when you can fit 4.
2 rotations on 1 side, 4 corners, 3 pieces and 2 sides. 2x4x3x2 = 48
48 + 1 combination when you can fit all = 49.
This is the logic calculation. If i did something wrong, tell me :P
Aaa edit. I forgot it doesn't need to be set in 90 degree angle.
so it's 4 rotations instead of 2
4x4x3x2 = 96
96+1 = 97
I'd guess it's 32*24*16*8 combinations, so 98304. But I'm no mathematician, so it's probably horribly wrong lol.
ZGoten it would be 4*4*4*2
Four pieces
Four corners
For rotations
Two sides
I don't think that's true. Once the first piece is set, you have only 3 corners for the next piece, then only 2, then only 1.
ZGoten that makes sense
98304 is right....i agree with you
-and then divide by 8 because the final puzzle can be turned and flipped. Giving 12288.
thank you for your videos, we ennjoy them very much
Thanks!
Total number of options is 98304, though very few of those would be solutions
2 sides * 4 rotations * n pieces left, n starts at 4 and reduces by one for each piece put in place=
2*4*4 * 2*4*3 * 2*4*2 * 2*4*1 = (8^4)*(4!) = 98304
There are 80 possible solutions (4 sides, top and bottom, and then 4 possible locations for the first piece, 3 for the second, 2 for the third, and 1 for the last).
EDIT: It's actually even fewer than that because the above calculation includes rotated versions of solutions, which one would likely not need to try if the frame is a proper square.
you are adding though 32+24+16+8, it's actually 32*24*16*8 :)
I guess this is not right solution
raszop
I thought that. It doesn't look right
raszop Your Pic is on my old school bag
+BzERK IE That's on purpose, I think, to make the puzzle harder. Because you will keep trying and trying to make the corners 'fit' the frame, and make all the edges meet. But the total area of the pieces is smaller than the area in the frame, so there must be gaps. The puzzle makers put the gaps in places you don't expect, to confuse you.
actually this would have been my first approach, too - look for rectangular corners in the pieces and dismiss all other positions... just to find out... one eternity later... that it is probably impossible to find a solution then ;)
I made this puzzle in my DT (woodwork, it might even be called something else where you're from) class when I was 14. You shouldn't need to jam anything in, and the trick is to ignore the holes altogether.
surprisingly counterintuitive from first appearance! great job
IT’S WOOD?! 😱I wished I knew that before I made my mom a sandwich. 😭
that puzzle is not so hard!
Therefore it's only a 3/5.
NoNo DaEnie .
we should see him solve life, iv'e barely got the first couple pieces in place ( i think)
NoNo DaEnie yes, is wood no metal
+Mr. Puzzle, 3/5? No dude, this is more like 1/10... even a child can solve it just by attempts and accuracy method!
Quite clever!
am I the only one who got goosebumps each time he would touch all four corners of the frame and center it?
This sounds soooo strange! :D
256 different ways to solve it
I am from germany
Zitrone250 ich auch
Alles Käse 🧀
Ja wa
Ich auch!
I am from Ukraine
each piece has 8 orientations and 4 possible positions so we get (8^4)*3!/2=12,288 possible unique solutions.
it is not 4! because that would include rotational symmetry, and it is divided by 2 for flipped symmetry.
this also assumes that the frame is perfectly square. if it is not, then... good luck on your 98,304 choices. hopefully there is more than 1 unique solution
The first corner could have 1 of any 4 pieces, in 1 of 2 directions in 1 of 4 rotations, making 32 potential combinations for the first corner. The second corner is the same with only 3 pieces, making 24, and the third corner has 16, then 8. Making in total, over 98,000 combinations!
Ob des jetzt Alles käse heißt oder Des macht kein Sinn, is mir doch Wurscht.
Alles Käse!
Err.... translation pls?
my calculations say 192 different possible combinations
1048576
how'd you get that?
Not exactly correct. Each piece has 8 ways to fit, 4 rotations on the front and. 4 on the back. The first piece has 4 places to go. 8*4. The second piece has the same 8 rotations, but now it only has 3 spaces to choose from. 8*3. The third piece has 8 orientations as well, but now only 2 spaces to fit in. 8*2. And finally, the last piece still has 8 possibilities, but only 1 space to go into. 8*1, or just 8. You find yourself with 8((8*4)(8*3)(8*2)), or 8((32)(24)(16)). This leaves you with the final result of 98,304 possibilities. (Trust me, I’m good with math)
Technically the first piece has only 1 place to go. And only 1 face. The frame is a square, all places are the same. One face or the other will only dictate which face the other pieces need to be placed.
So only rotation count for the first piece, therefore only 4 possibilities.
For the other pieces you can apply your logic
The Crafted Warriors forgot about the isomorphisms between the two. For any orientation, there are 7 others exactly like it (pieces in rotated corners and also everything mirrored) This makes for that number divided by 8
3! * (2*4)^4 = 24576 possibilities
w.l.o.g. assume the red part is on the top left (so we don't have to deal with rotations)
3! = 6 possibilities to arrange the other 3 parts
each part has 2 sides and 4 orientations => 8 ways to put it
those 8 ways can be applied seperately to all 4 pieces
Almost correct. The correct answer is half. You can wlog assume that the red part also has a specific side up. -OR you can divide by two in the end because the puzzle can be turned bottom up(still with red part in top left).
The total possible solutions would be 8^4 * 3 * 2 which would be just under 25,000.
I dont speak japanese
True story
I guess there are a lot of people who do not speak Japanese.
Yes Another Ding At Lunchtime 😮😮😮😀👨🏼🔧👩🏻🔧 It’s Mr Puzzle Uploaded a New Amazing Video Yesssss Me n The Mrs Love Your Puzzling Puzzles Mr Puzzle 😀😮😅👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼👍🏼 Thumbs Up Thanks Again Happy Puzzling 😀😀👩🏻🔧👨🏼🔧
The hell?
Yeah! Enjoy your Friday puzzling lunch break!
Regards to both of you!
Mr.Puzzle Thank You 😀👩🏻🔧👨🏼🔧
Sebastian Leaf we have spotted a normie
Please use correct capitalization... also, you don't need that many emojis. Sorry, it just... really bugs me.
Combination totals can be found using probability with three factors: the piece, the rotation, and the place. You would start with 4 x 4 x 4 which is 64. Then, you would have 3 x 4 x 3, 2 x 4 x 2, and 1 x 4 x 1. This all adds up to 64 x 36 x 16 x 4 which is 147,456 outcomes in all
Possible (unique) placements; 12288:
1) In one corner, you can place 1 piece in 4 different rotations. Then you can flip it, and have 4 new rotations. 8 total possibilities so far.
2) You can place that 1st piece in one of the 4 corners, in one of the 8 ways. 4*8=32 possibilities for 1st piece.
3) You can place second piece in one of the reminding 3 corners, in one of the 8 ways. 3*8=24 possibilities for 2nd piece.
4) Going by this, piece 3 can be placed 16 ways, and reminding one only 8 ways. 32*24*16*8=98304 possible (total) solutions
5) some of the solutions are actually similar, because like with the 1 piece, you can have solution to be rotated in 4 different rotations. Then you can flip it, and have 4 new rotations.
-Giving total of 8 repetition for each solution.
6)98304/8=12288
80 ways i calculated
lol
Try like 12,000.
(2*4*4)*(2*4*3)*(2*4*2)*(2*4)=98 thousand
(2*4*4)^4
hmm i imagined every combination in my brain idk if im right
8 (possibilities for the first piece) x 6 (for the second...) x 4 (for the third) x 2 (for the last) = 384
These are simplistic possibilities that ignore the (graduated) _horizontal_ and (miniscule, and graduated rotational) translations that are both possible, and actually _necessary_ for the solution.
This is only true if you don't consider that you can rotate each piece by 90, 180 or 270 degrees.
Additionally, you need to divide by 4 at the end, because you can rotate the whole frame to turn one configuration into another, therefore counting every configuration 4 times
nonono. Each piece can be arranged in a corner in 8 ways (2 for flipping the piece, 4 for rotation), so in each corner you have 8 possibilities. Firstly, there are 4 possibilities, so we multiply by four to account for all of them (2*4*4) then there are 3 possibilities so we have to multiply by 3 and so on. The last expression can be simplified to 4!.
there are 2*4*4! or 192 different possibilities
Each piece has 8 ways to fit, 4 rotations on the front and. 4 on the back. The first piece has 4 places to go. 8*4. The second piece has the same 8 rotations, but now it only has 3 spaces to choose from. 8*3. The third piece has 8 orientations as well, but now only 2 spaces to fit in. 8*2. And finally, the last piece still has 8 possibilities, but only 1 space to go into. 8*1, or just 8. You find yourself with 8((8*4)(8*3)(8*2)), or 8((32)(24)(16)). This leaves you with the final result of 98,304 possibilities. (Trust me, I’m good with math)
No offense, but thats completely wrong. Each piece has 8 ways to fit, 4 rotations on the front and. 4 on the back. The first piece has 4 places to go. 8*4. The second piece has the same 8 rotations, but now it only has 3 spaces to choose from. 8*3. The third piece has 8 orientations as well, but now only 2 spaces to fit in. 8*2. And finally, the last piece still has 8 possibilities, but only 1 space to go into. 8*1, or just 8. You find yourself with 8((8*4)(8*3)(8*2)), or 8((32)(24)(16)). This leaves you with the final result of 98,304 possibilities. (Trust me, I’m good with math)
really strange but interesting solution.
Good video!
My Math
(cab) x (dab) x (eab) x (fab)
a = sides on each piece(you can flip one piece over to make the reverse of a piece)
b = orientation in each corner(four ways to orient each piece on one side)
c,d,e,f = corners left to put pieces in (on the board)
(¼ x ½ x ¼)(⅓ x ½ x ¼)(½ x ½ x ¼)(½ x ¼)
(1/32)(1/24)(1/16)(1/8)
(1/768)(1/128)
1/98,304
Sorry but this is NOT the correct solution. Surely all the holes on the sides of the pieces of 'cheese' need to align up?
No, this is not part pf the solution.
Theyre different cheeses, not one goant multicolored cheese
That would make it too easy
If you look at the holes, you will quickly notice that the cheese holes are all different sizes, and the positions don't match. They are a detail added for confusion, the make the puzzle more difficult.
The number of variants is exactly 8. That puts each niece in each of the four corners, plus those same corners inverted.
Is there a file that I can download to make my own on my own laser cutter?
I am seeing loads of different calculations. Would very much like to know which is true.
This is my working out:
There are 24 possible ways you can order 4 pieces. I.E. 4 * 3 * 2 * 1 or 4!
Each piece has 8 possible rotations.
8^4 possible rotation states (4096) but if you think about it the problem is symmetric. If I solved it then glued the pieces together and flipped them over it would still fit. In fact because it's a square you can rotate the newly glued piece in 8 permutations and it would fit. 4096 ÷ 8 = 512.
So you have 24 ways to arrange the pieces and 512 possible ways they can be rotated.
24 * 512 = 12,288
I like how you said "Siebenstein Spiele". Really cool puzzle, man!
Total combinations : 4x3x2x (4^4)*(2^4)= 98304 (for 4 squares of course)
Hits quite easy, I solved it already before half of the video.
I Love puzzles 😀😺 I've always wanted to try playing different one's 😸😄
There are 4 parts, each with 8 orientations: being face up or face down in any of four corners, this is for the first piece of the puzzle, after which we move to the second piece, which now has six orientations: face up or down in any of the remaining three corners. Third piece has four orientations and the last piece has two, accordingly.
Put in an equation, x=(4(8)3(8)2(8)8)*(3(6)2(6)6)*(2(4)^2)*2, where X is the total number of possible unique combinations if order of placement matters, supposing all pieces fit correctly.
That mess reduces down to 8,152,726,976. That's super high, but again, that is assuming the order matters AND all the pieces fit, both of which drastically increase the number of possible solutions.
I do not have the puzzle here, but from the face of it, it would seem that your solution would fit more easily rotated 90° counter clockwise, as the lengths of the sides of the frame seem to differ: top is the longest and right the shortest.
There are 4 parts, they can be placed on 4 different places (4*4), they can be rolled clockwise or counterclockwise (4*4*4*4) and because you can flip them over (4*4*4*4)^2. In my opinion the maximum variants for solving this puzzle are 65 536 (it will take 0.3125 seconds to computer for solving it)
So because each piece has 32 different placements (4 on one side, 4 on the other, for each corner of the board), that means there's 128! (Factorial) different ways to place the pieces. Just to show the magnitude of how huge that is, this is the number 385620482362580421735677065923463640617493109590223590278828403276373402575165543560686168588507361534030051833058916347592172932262498857766114955245039357760034644709279247692495585280000000000000000000000000000000. If you wanna know how big that is, watch the Vsauce video on what 52! Is and times his ways of explaining it by 1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000. It is insane how many ways this puzzle could go
Merci mr puzzle
hmmm this puzzle must have more solutions, because I found one that makes all the holes in the sides of the pieces actually match up.
There are 4! = 4*3*2*1 = 24 possible positions, without considering orientation yet. There are 8 orientations (4 directions and their reflections) for each piece, so for 4 pieces there are 8^4 possibilities.
So the solution is 4! * 8^4 = 98304 combinations.
The total number of possible arrangements of the pieces = 2^4 * 4^4 * 3!
= 4^2 * 4^4 * 3 * 2 * 1
= 4^6 * 6
= 24 576.
Explanation: Where does 2^4 come from? Each piece can be flipped one way or the other, so with two possible sides for each of the four pieces that gives 2^4 combinations of flipped pieces.
What about the 4^4? This is for the rotation of the pieces. Each piece has four sides, so each has four rotations that changes how the sides align with the other pieces.
The 3! is not just an excited 3, the exclamation mark is used in mathematics to represent a "factorial" this means multiplying a number by every integer less than it and greater than 0; in this case 3! = 3 * 2 * 1 = 6. Okay so why use factorial and why 3? It is 3 because the first piece can go anywhere, the frame is symmetrical so it doesn't matter which corner we start in, what matters is how the remaining 3 pieces relate to the first. Why factorial? The factorial of a number n gives us the number of permutations of a set of n objects; try it yourself with 2, 3, 4, 5 for example, pretty amazing.
Finally we take the product of these three values because for each combination of flips we can have all possible rotations and all possible positions, and vice versa.
I think maybe divide this by 2 is correct because that relates to flipping the entire puzzle over which changes nothing about the relative positions and orientations.
Why not 4! ? Since there are 4 corners?
tom smith I allowed the first piece to start in any corner. That is the same as rotating the whole puzzle.
Remember, the amount of pieces is 4, so you square it as one piece could stay the same with 4 different combinations of the others and then times your answer by 4 again, as the same thing could happen just with different positions. 4 squared = 16. 16×4=64. If you add the rotations, every piece can rotate 4 times. At the beginning of my comment the first piece that was squared could be different, therefore different rotations. You would times 64 by 32. 64×32= 2048. 2048 is the maximum combination
The thing that would confuse me initially is that the pieces don't fit exactly in the corners! Very clever!
Favorite past is how he says Mr. Puzzle.
ich finde es immer lustig, wie man direkt an der Aussprache merkt, dass da ein Deutscher Englisch spricht :D
ich mag dieses Platte Deutsch/Englisch :D
Und ich dachte ich wäre der einzige der das hört
I find they all fit in if you stack them on top of one another.