Add project files.

8Queens.sln

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+
+Microsoft Visual Studio Solution File, Format Version 12.00
+# Visual Studio Version 17
+VisualStudioVersion = 17.1.32407.343
+MinimumVisualStudioVersion = 10.0.40219.1
+Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "8Queens", "8Queens\8Queens.csproj", "{9DBA6583-0244-44C7-974C-DBD0F46D3F03}"
+EndProject
+Global
+	GlobalSection(SolutionConfigurationPlatforms) = preSolution
+		Debug|Any CPU = Debug|Any CPU
+		Release|Any CPU = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(ProjectConfigurationPlatforms) = postSolution
+		{9DBA6583-0244-44C7-974C-DBD0F46D3F03}.Debug|Any CPU.ActiveCfg = Debug|Any CPU
+		{9DBA6583-0244-44C7-974C-DBD0F46D3F03}.Debug|Any CPU.Build.0 = Debug|Any CPU
+		{9DBA6583-0244-44C7-974C-DBD0F46D3F03}.Release|Any CPU.ActiveCfg = Release|Any CPU
+		{9DBA6583-0244-44C7-974C-DBD0F46D3F03}.Release|Any CPU.Build.0 = Release|Any CPU
+	EndGlobalSection
+	GlobalSection(SolutionProperties) = preSolution
+		HideSolutionNode = FALSE
+	EndGlobalSection
+	GlobalSection(ExtensibilityGlobals) = postSolution
+		SolutionGuid = {E3A02A7B-D4EC-4081-B993-BA904AE54F36}
+	EndGlobalSection
+EndGlobal

8Queens/8Queens.csproj

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+<Project Sdk="Microsoft.NET.Sdk">
+
+  <PropertyGroup>
+    <OutputType>WinExe</OutputType>
+    <TargetFramework>net6.0-windows</TargetFramework>
+    <RootNamespace>_8Queens</RootNamespace>
+    <Nullable>enable</Nullable>
+    <UseWPF>true</UseWPF>
+  </PropertyGroup>
+
+  <ItemGroup>
+    <None Remove="ChessQueen.png" />
+  </ItemGroup>
+
+  <ItemGroup>
+    <Resource Include="ChessQueen.png" />
+  </ItemGroup>
+
+</Project>

8Queens/App.xaml

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+<Application x:Class="_8Queens.App"
+             xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
+             xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
+             xmlns:local="clr-namespace:_8Queens"
+             StartupUri="MainWindow.xaml">
+    <Application.Resources>
+    </Application.Resources>
+</Application>

8Queens/App.xaml.cs

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+using System;
+using System.Collections.Generic;
+using System.Configuration;
+using System.Data;
+using System.Linq;
+using System.Threading.Tasks;
+using System.Windows;
+
+namespace _8Queens
+{
+    /// <summary>
+    /// Interaction logic for App.xaml
+    /// </summary>
+    public partial class App : Application
+    {
+    }
+}

8Queens/AssemblyInfo.cs

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+using System.Windows;
+
+[assembly: ThemeInfo(
+    ResourceDictionaryLocation.None, //where theme specific resource dictionaries are located
+                                     //(used if a resource is not found in the page,
+                                     // or application resource dictionaries)
+    ResourceDictionaryLocation.SourceAssembly //where the generic resource dictionary is located
+                                              //(used if a resource is not found in the page,
+                                              // app, or any theme specific resource dictionaries)
+)]

8Queens/Board.cs

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+using System.Collections.Generic;
+
+namespace _8Queens
+{
+    public class MainViewModel 
+    {
+        const int MAX = 8;
+
+        public int[,] Board;
+        public List<List<Cell>> CellBoard = new();
+
+        //ctor - builds the chessboard
+        public MainViewModel()
+        {
+            CellBoard = new List<List<Cell>>(MAX);
+
+            for (int i = 0; i < MAX; i++)
+            {
+                CellBoard.Add(new List<Cell>(MAX));
+
+                for (int j = 0; j < MAX; j++)
+                {
+                    CellBoard[i].Add(new Cell());
+                }
+            }
+
+            Board = new int[MAX, MAX];
+        }
+        public bool Solve(int col)
+        {
+            //if all queens are placed return true
+            if (col >= MAX)
+            {
+                return true;
+            }
+
+            for (int row = 0; row < MAX; row++)
+            {
+                if (IsSafe(row, col))
+                {
+                    Board[row, col] = 1;
+                    CellBoard[row][col].Value = 1;
+
+                    if (Solve(col + 1))
+                    {
+                        return true;
+                    }
+
+                    Board[row, col] = 0;
+                    CellBoard[row][col].Value = 0;
+                }
+            }
+            return false;
+        }
+
+        bool IsSafe(int row, int col)
+        {
+            //from the left until the current col
+            for (int i = 0; i < col; i++)
+            {
+                if (Board[row, i] == 1)
+                {
+                    return false;
+                }
+            }
+
+            //upper diagonal
+            for (int i = row, j = col; i >= 0 && j >= 0; i--, j--)
+            {
+                if (Board[i, j] == 1)
+                {
+                    return false;
+                }
+            }
+
+            //lower diagonal
+            for (int i = row, j = col; i < MAX && j >= 0; i++, j--)
+            {
+                if (Board[i, j] == 1)
+                {
+                    return false;
+                }
+            }
+            return true;
+        }
+    }
+}
+

8Queens/Cell.cs

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+namespace _8Queens
+{
+    public class Cell 
+    {
+        private int _value;
+
+        public int Value
+        {
+            get => _value;
+            set => _value = value;
+        }
+    }
+}