This code results in No solution found, which is not correct. I just need help with the logic.

public class House $\{$

String color;

String nationality;

String drink;

String cigar;

String pet;

public House$($String color, String nationality, String drink, String cigar, String pet$)\{$

this.color $=$ color;

this.nationality $=$ nationality;

this.drink $=$ drink;

this.cigar $=$ cigar;

this.pet $=$ pet;

$\}$

$\}$

public class Solution $\{$

static String$[]$ possibleColors $=\{"$red$",$ "green", "white", "yellow", "blue"$\}$;

static String$[]$ possibleNationalities $=\{"$Brit$",$ "Swede", "Dane", "Norwegian", "German"$\}$;

static String$[]$ possibleDrinks $=\{"$tea$",$ "coffee", "milk", "beer", "water"$\}$;

static String$[]$ possibleCigars $=\{"$Pall Mall", "Dunhill", "Blends", "Bluemasters", "Princes"$\}$;

static String$[]$ possiblePets $=\{"$dogs$",$ "birds", "cats", "horses", "fish"$\}$;

public static boolean solveRiddle$($House$[]$ houses, int index$)\{$

if $($index $==5)\{$

return true; $//$ Base case: all houses have been assigned attributes

$\}$

$//$ Try all possible attributes for the current house

for $($String color : possibleColors$)\{$

for $($String nationality : possibleNationalities$)\{$

for $($String drink : possibleDrinks$)\{$

for $($String cigar : possibleCigars$)\{$

for $($String pet : possiblePets$)\{$

houses$[$index$]=$ new House$($color$,$ nationality, drink, cigar, pet$)$;

$//$ Check if the current assignment satisfies all constraints

if $($isValid$($houses$,$ index$)$ && solveRiddle$($houses$,$ index $+1))\{$

return true; $//$ Found a valid solution

$\}$

$\}$

$\}$

$\}$

$\}$

$\}$

return false; $//$ No valid solution found, backtrack

$\}$

public static boolean isValid$($House$[]$ houses, int index$)\{$

$//$ Apply the given clues as constraints

$//$ Clue $1$: The Brit lives in the red house

if $($houses$[$index$].$nationality.equals$("$Brit$")$ && $!$houses$[$index$].$color.equals$("$red$"))\{$

return false;

$\}$

$//$ Clue $2$: The Swede keeps dogs as pets

if $($houses$[$index$].$nationality.equals$("$Swede$")$ && $!$houses$[$index$].$pet.equals$("$dogs$"))\{$

return false;

$\}$

$//$ Add more constraints for the remaining clues

$//$ Clue $3$: The dane drinks tea

if $($houses$[$index$].$nationality.equals$("$Dane$")$ && $!$houses$[$index$].$drink.equals$("$tea$"))\{$

return false;

$\}$

$//$ Clue $4$: The green house is on the left of and next to the white house

if$($houses$[$index$].$color.equals$("$green$")$ && houses$[$index $+1].$color.equals$("$white$"))\{$

return false;

$\}$

$//$ Clue $5$: The green house owner drinks coffee

if$($houses$[$index$].$color.equals$("$green$")$ && $!$houses$[$index$].$drink.equals$("$coffee$"))\{$

return false;

$\}$

$//$ Clue $6$: The person who smokes Pall Malls keeps birds

if$($houses$[$index$].$cigar.equals$("$Pall Mall"$)$ && $!$houses$[$index$].$pet.equals$("$birds$"))\{$

return false;

$\}$

$//$ Clue $7$: The owner of the yellow house smokes Dunhills

if$($houses$[$index$].$color.equals$("$yellow$")$ && $!$houses$[$index$].$cigar.equals$("$Dunhill$"))\{$

return false;

$\}$

$//$ Clue $8$: The man living in the house right in the center drinks milk

if$($index $==2$ && $!$houses$[$index$].$drink.equals$("$milk$"))\{$

return false;

$\}$

$//$ Clue $9$: The man who smokes Blends lives next to the one who keeps cats

if$($houses$[$index$].$cigar.equals$("$Blends$")$ && houses$[$index $+1].$pet.equals$("$cats$"))\{$

return false;

$\}$

$//$ Clue $10$: The Norwegian lives in the first house

if$($index $==0$ && $!$houses$[$index$].$nationality.equals$("$Norwegian$"))\{$

return false;

$\}$

$//$ Clue $11$: The man who keeps horses lives next to the one who smokes Dunhills

if$($houses$[$index$].$pet.equals$("$horses$")$ && houses$[$index $+1].$cigar.equals$("$Dunhill$"))\{$

return false;

$\}$

$//$ Clue $12$: The owner who smokes Bluemasters drinks beer

if$($houses$[$index$].$cigar.equals$("$Bluemasters$")$ && $!$houses$[$index$].$drink.equals$("$beer$"))\{$

return false;

$\}$

$//$ Clue $13$: The German smokes Princes

if$($houses$[$index$].$nationality.equals$("$German$")$ && $!$houses$[$index$].$cigar.equals$("$Princes$"))\{$

return false;

$\}$

$//$ Clue $14$: The Norwegian lives next to the blue house

if$($houses$[$index$].$nationality.equals$("$Norwegian$")$ && houses$[$index $+1].$color.equals$("$blue$"))\{$

return false;

$\}$

$//$ Clue $15$: The man who smokes Blends has a neighbor who drinks water

if$($houses$[$index$].$cigar.equals$("$Blends$")$ && houses$[$index $+1].$drink.equals$("$water$"))\{$

return false;

$\}$

return true;

$\}$

public static void main$($String$[]$ args$)\{$