This version handles the initiation of the 15 puzzle through cloning and applying the right - premade - costume to each clone.
The positions of all slides are collected into a list called RowList - containing id, row, column, xpos, ypos.
The gap is item 16.
At clicking the neighbours are checked through a double keep items (see nextToGap). If the gap is neighbouring, the swap between the clicked slide and the gap is done. The positions in Rowlist are updated.
The scrambling is done through a list of 16 unique numbers.
IIt has taken a really long time to find the definitive answer as to when a sliding puzzle is solvable and when not. I found the answer in a sliding puzzle assignment from Princeton University. I quote their answers below:
"Odd-sized boards. First, we’ll consider the case when the board size n is an odd integer. In this case, each move changes the number of inversions by an even number. Thus, if a board has an odd number of inversions, it is unsolvable because the goal board has an even number (zero) of inversions. It turns out that the converse is also true: if a board has an even number of inversions, then it is solvable.In summary, when n is odd, an n-by-n board is solvable if and only if its number of inversions is even."
"Even-sized boards. Now, we’ll consider the case when the board size n is an even integer. In this case, the parity of the number of inversions is not invariant. However, the parity of the number of inversions plus the row of the blank square (indexed starting at 0) is invariant: each move changes this sum by an even number.
That is, when n is even, an n-by-n board is solvable if and only if the number of inversions plus the row of the blank square is odd."
N.B. the row of the blank square is counted from the top, index starting at 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 version handles the initiation of the 15 puzzle through cloning and applying the right - premade - costume to each clone.
The positions of all slides are collected into a list called RowList - containing id, row, column, xpos, ypos.
The gap is item 16.
At clicking the neighbours are checked through a double keep items (see nextToGap). If the gap is neighbouring, the swap between the clicked slide and the gap is done. The positions in Rowlist are updated.
The scrambling is done through a list of 16 unique numbers.
IIt has taken a really long time to find the definitive answer as to when a sliding puzzle is solvable and when not. I found the answer in a sliding puzzle assignment from Princeton University. I quote their answers below:
"Odd-sized boards. First, we’ll consider the case when the board size n is an odd integer. In this case, each move changes the number of inversions by an even number. Thus, if a board has an odd number of inversions, it is unsolvable because the goal board has an even number (zero) of inversions. It turns out that the converse is also true: if a board has an even number of inversions, then it is solvable.In summary, when n is odd, an n-by-n board is solvable if and only if its number of inversions is even."
"Even-sized boards. Now, we’ll consider the case when the board size n is an even integer. In this case, the parity of the number of inversions is not invariant. However, the parity of the number of inversions plus the row of the blank square (indexed starting at 0) is invariant: each move changes this sum by an even number.
That is, when n is even, an n-by-n board is solvable if and only if the number of inversions plus the row of the blank square is odd."
N.B. the row of the blank square is counted from the top, index starting at 0This block creates new variables on the selected scope: global (for all sprites), sprite (for this sprite only) or script (only for that blocks stack) with the names given (in 'names' list).
If there is already a variable with that name in that scope, it does nothing: no errors and no overwrites.pt:cria as variáveis _ _
ca:crea les _ variables _
es:crear las _ variables _
de:erstellen _ var _
pl:utwórz zmienną _ _
globalglobal
sprite
scriptThis block deletes all the variables with the names given (inside input list).
Each name will make only one variable deletion, and this will be the variable found following the scope order: 'script' -> 'sprite' -> 'global'.
If we have a "testing" sprite variable and also a "testing" global one, deleting "testing" will delete only the sprite one (Yes! we can also do "delete var (testing, testing)" to delete both.
If one variable does not exists (in any scope) an error happens, stopping block action in that point. You can check it before with the "does var (name) exists?"block. pt:remove as variáveis _
ca:esborra les variables _
es:borrar variables _
de:löschen var _
pl:usuń zmienną _
This block sets the given value (last input) to the variable named with the name givent (var input).
It looks for that variable following the scope order 'script' -> 'sprite' -> 'global' (the first match it finds).
If that variable does not exist (in any scope) an error happens, stopping their script. You can check it before using the "does var (name) exists?" block. ca:assigna a _ el valor _
es:asignar a _ el valor _
pt:altera _ para _
de:setze var _ auf _
pl:ustaw zmienną _ na _
§_getVarNamesDictThis block reports the value of the variable with the name given.
It looks for that variable following the scope order 'script' -> 'sprite' -> 'global' (the first match it finds).
If that variable does not exist (in any scope) an error happens, stopping their script. You can check it before using the "does var (name) exists?" block. pt:o valor de _
pl:zmienna _
§_getVarNamesDictThis block reports "true" if there is a variable with this given name (input slot) in that context.
It can be a global, sprite or script variable.
Otherwise it reports "false".pt:a variável _ existe
ca:existeix la variable _ ?
es:existe la variable _ ?
de:existiert var _ ?
pl:zmienna _ istnieje?
err_resetThis block turns on (show) the watcher view on stage (if it was not already activated) of the variable with the given name (slot input).
It can only access to the closest variable scope (if there different variables with the same name in different scopes) following the order 'script' -> 'sprite' -> 'global'.
No errors if that variable does not exist.ca:mostra la variable _
es:mostrar variable _
pt:mostra a variável _
de:zeige var _
pl:pokaż zmienną _
§_getVarNamesDictThis block turns off (hide) the watcher view on stage (if it was not already activated) of the variable with the given name (slot input).
It can only access to the closest variable scope (if there different variables with the same name in different scopes) following the order 'script' -> 'sprite' -> 'global'.
No errors if that variable does not exist.ca:amaga la variable _
es:esconder variable _
pt:esconde a variável _
de:verstecke var _
pl:ukryj zmienną _
§_getVarNamesDictde:Kostüm aus Text _ Größe _
pt:um traje com o texto _ de tamanho _
ca:vestit amb el text _ i mida _
A72xydircstpen state90trailsStage0Stage0costumeobj_name(obj, name)pl:kostium _ z tłem RGBA _ rozmiar tła _
§_costumesMenu2002Use this block to make "clickable" buttons:de:fange _ _
ca:agafa _ _
es:atrapar _ _
fr:attrape _ _
pt:captura _ _
pl:przechwyć _ _
contde:wirf _
ca:llança _
es:lanzar _
fr:lance _
pt:lança _
pl:wyrzuć _
catchtagde:fange _ _
ca:agafa _ _
es:atrapar _ _
fr:attrape _ _
pt:captura _ _
pl:przechwyć _ _
contde:wirf _ _
ca:llança _ _
es:lanzar _ _
fr:lance _ _
pt:lança _ _
pl:wyrzuć _ _
catchtagThis is a breakpoint block, to be used in debugging.
The Boolean input specifies the condition under which
the program should pause. (Use True for an unconditional breakpoint.) The intent is that the script should have
SHOW VARIABLE blocks for the process's local variables.
After the pause, this block automatically hides all temporary variables.de:falls _ dann _ und pause $pause-1-255-220-0
ca:si _ fes _ i atura-ho tot $pause-1-255-220-0
es:si _ haz _ y páralo todo $pause-1-255-220-0
fr:si _ faire _ et mettre tout en pause $pause-1-255-220-0
pt:se _ , então _ e faz pausa em tudo $pause-1-255-220-0
pl:jeżeli _ wykonaj _ i pauzuj wszystko $pause-1-255-220-0
This block does nothing.
Use it when you are calling a reporter
for its side effect and don't care about
its return value.de:ignoriere _
ca:ignora _
es:ignorar _
fr:ignore _
pt:ignora _
pl:ignoruj _
Call f(f(f(...(f(x))))) n times where the three input slots are n, f, and x from left to right. The # variable can be used inside f to represent how many times f has been called.pt:o resultado de _ invocações em cascata de _ com argumento inicial _ _
ca:en cascada _ vegades _ _ _
pl:kaskada _ razy _ _ _
Call f(f(f(...(f(x))))) until condition is true, where the three input slots are condition, f, and x from left to right. The # variable can be used inside f or condition to indicate how many times f has been called.pt:o resultado da invocação em cascata até que _ de _ com argumento inicial _ _
ca:en cascada fins _ _ _ _
pl:kaskada aż _ _ _ _
Returns the function x↦f(g(x)) where f and g are the two inputs.pt:a composição de _ com _
ca:composa _ _
pl:skomponuj _ _
Like the built-in REPEAT UNTIL block, except that the ending condition is not tested until the script has been run the first time. So the script is run at least once.pt:repete _ até que _ $loop-0.7
ca:repeteix _ fins _
pl:powtarzaj _ aż _
Run the script repeatedly, as long as the given condition is true. Runs the script at least once before testing the condition.pt:repete _ enquanto _ $loop-0.7
ca:repeteix _ mentre _
pl:powtarzaj _ gdy _
Runs the script repeatedly, as long as the condition is true. Tests the condition before the first time the script is run. Like the built in REPEAT UNTIL except that in this block the condition must be true, not false.pt:enquanto _ , repete _ $loop-0.7
pl:powtarzaj gdy _ _
Runs the script the specified number of times, like the built-in REPEAT block, but this one provides the # variable that can be used inside the script. Try
REPEAT (200)
MOVE (#) STEPS
RIGHT 92
with the pen down.pt:repete _ vezes _ _ $loop-0.7
ca:repeteix _ _ _
pl:powtórz _ _ _
The primitive FOR block uses an implicit step of ±1 depending on which of the starting and ending values is larger. This version allows you to provide an explicit step value. If the sign of the step input is incompatible with the ordering of the starting and ending values, the script will not be run at all.pt:para _ de _ com passo _ a _ _ $loop-0.7
ca:per _ = _ incrementant _ fins _ _
pl:dla _ = _ co _ do _ _
1110Provides LOOP as a function of one input that runs
the body of the LET with A set to the function input,
so the body can run itself recursively.
See COPY block in Variables for an example of use.pt:tendo _ o valor inicial _ , executa _ definido como _
ca:fes que _ sigui _ al _ _
pl:ustaw _ na _ w _ _
new valuede:führe _ mit Continuation aus
de:rufe _ mit Continuation auf
pieces are already in positioncloneListi1slideRow2slideColumn3slideXpos4slideYpos516234566to make sure this column does not disturb the comparison between starlist and rowlist216316416516Reports a sorted version of the list in its first input slot, using the comparison function in the second input slot. For a list of numbers, using < as the comparison function will sort from low to high; using > will sort from high to low.ca:ordena _ segons criteri _
pl:$flash sortuj _ za pomocą _
The second input is an "association list," a list of two-item lists. Each of those smaller lists has a "key" as its first item and a "value" as its second. ASSOC reports the first key-value pair in the association list whose key matches the first input.ca:associació _ _
pl:$flash skojarz _ _
This block carries out the given script for each item of the given list, like the primitive FOR EACH.
What's different is that it provides the # variable, which will contain the item number in the list of each item in turn, 1 while processing item 1, and so on.ca:_ per cada _ de _ _
pl:_ dla każdego _ z _ _
1Takes a (possibly deep) list as input,
and reports a human-readable text form
of the list (namely, Lisp notation).
Will not work on circular lists.ca:notació textual de _
pl:tekstowa _
()SENTENCE is the main constructor for sentences, represented
as lists of words. It takes zero or more inputs, each of which can
be either a list or a text string. If a list, the input is assumed to be
a list of words. If a text string, it is converted to a list of words using
SENTENCE→LIST. Then all the lists of words are appended to form a new list of words.
If the inputs are lists of lists rather than lists of words, SENTENCE,
like APPEND, does only one level of flattening, reporting a list of
all the items of all the input lists.ca:frase _
pl:zdanie _
ZIP takes any number of lists as inputs. The lists should all be the same length. ZIP reports a list of lists in which the first item is a list of all the first items, the second item is a list of all the second items, etc.
Viewing the inputs as the rows of a matrix, ZIP reports its transpose.pl:$flash spakuj _
The identity function reports its input.Takes as input a function of N inputs and N lists.
The function is called with item 1 of all the lists as its inputs, with item 2 of all the lists as its inputs, and so on. (The lists should all be the same length.)ca:multi-mapeja _ sobre _
pl:mapuj wielokrotnie _ na _
Takes a sentence in text string form and reports the sentence as a list of its words.de:Satz $arrowRight Liste _
ca:frase $arrowRight llista _
es:frase $arrowRight lista _
fr:phrase $arrowRight liste _
pt:uma lista com as palavras da frase _
pl:zdanie $arrowRight lista _
116determine nr of puzzle inversionsgRow1gaprow is counted from the top - upper row is indexed with 0update rowlist positionscnt1give them all new positionsk11gapgapRow2gapColumn3gapX4gapY5gapPos6trueslideslideRow2slideColumn3trueslideXpos4slideYpos5slidePos62345623456Allows reading global settings programmatically.
Eisenberg's Law: Anything you can do from the user interface you should be able to do in your program, and vice versa. This library is just a beginning; there are many UI controls outside of the Settings menu.pt:o valor da configuração _
ca:paràmetre _
pl:ustawienie _
Project notes
Project name
User
Presentation mode
Language
Zoom blocks
Stage size
Stage scale
Retina display support
Long form input dialog
Plain prototype labels
Input sliders
Execute on slider change
Clicking sound
Turbo mode
Flat design
Keyboard editing
Visible stepping
Thread safe scripts
Prefer smooth animations
Flat line ends
Codification support
Inheritance support
Hyper blocks support
Visible paletteAllows changing global settings programmatically.
This block is for Boolean (checkbox) settings; use
SET VALUE for numeric or text values.
Eisenberg's Law: Anything you can do from the user interface you should be able to do in your program, and vice versa. This library is just a beginning; there are many UI controls outside of the Settings menu.pt:altera o valor da configuração _ para _
ca:fixa el paràmetre _ a _
pl:ustaw flagę _ na _
Presentation mode
Retina display support
Long form input dialog
Plain prototype labels
Input sliders
Execute on slider change
Clicking sound
Turbo mode
Flat design
Keyboard editing
Visible stepping
Thread safe scripts
Prefer smooth animations
Flat line ends
Codification support
Inheritance support
Hyper blocks supportAllows changing global settings programmatically.
This block is for numeric or text settings; use
SET FLAG for Boolean (checkbox) values.
Eisenberg's Law: Anything you can do from the user interface you should be able to do in your program, and vice versa. This library is just a beginning; there are many UI controls outside of the Settings menu.pt:altera o valor da configuração _ para _
ca:fixa el valor de _ a _
pl:ustaw wartość _ na _
Project notes
Project name
Language
Zoom blocks
Stage size
Stage scale
Visible 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1234562345645true1myOthClonesmyOthClonesxTempfalseslideRowslideColumnslideXslideYslidePos1234562345645trueactiveItem1684-8440444repaired the calculation of g-row once more.
Was taken from the wrong list (rowList) that wasn't repaired through repairList when I calculated the gRow value.
TODO: Move a whole range of slides (row)/(column) at onceParitychecks are done here. According to Princeton University:
* When n is odd, an n-by-n board is solvable if and only if its number of inversions is even
* When n is even, an n-by-n board is solvable if and only if the number of inversions plus the row of the blank square is odd.
The row of the blank square is counted from the top, indexed starting at 0 (top row is row 0).
This seems to be the only correct way of establishing solvability. Forget all the other advice gemini gives to you. There is this habit of everyone repeating the info they find without proper testing that makes it difficult to shake off / get rid of the incorrect information.164-84,842442-84841,3,4,84,-42,342,1,2,0,42,123,4,3,42,-84,434,3,3,42,-42,335,2,2,0,0,226,1,1,-42,42,117,1,4,84,42,148,2,4,84,0,249,3,1,-42,-42,3110,4,2,0,-84,4211,4,1,-42,-84,4112,2,1,-42,0,2113,4,4,84,-84,4414,3,2,0,-42,3215,1,3,42,42,1316,2,3,42,0,2316,2,1,-42,0,2112,2,2,0,0,225,2,3,42,0,2342022230022,2,1,-42,12,40false1,1,1,-42,42,112,1,2,0,42,123,1,3,42,42,134,1,4,84,42,145,2,1,-42,0,216,2,2,0,0,227,2,3,42,0,238,2,4,84,0,249,3,1,-42,-42,3110,3,2,0,-42,3211,3,3,42,-42,3312,3,4,84,-42,3413,4,1,-42,-84,4114,4,2,0,-84,4215,4,3,42,-84,4316,4,4,84,-84,4416,4,4,84,-7216,4,1,-41.999999999999986,-71.99999999999999falsetrue16492922237,3,2,0,-42,320,10,20,30,40,50,60,70,80,90,100,110,120,140,150,16123456789101112131415166,2,15,7,9,12,5,8,11,16,4,1,10,14,3,13