Improve solver (WIP, currently broken)

domain/src/main/kotlin/ch/dissem/yaep/domain/generator.kt

@@ -1,6 +1,8 @@
 package ch.dissem.yaep.domain
 
-import ch.dissem.yaep.domain.PuzzleSolution.*
+import ch.dissem.yaep.domain.PuzzleSolution.MULTIPLE_SOLUTIONS
+import ch.dissem.yaep.domain.PuzzleSolution.NO_SOLUTION
+import ch.dissem.yaep.domain.PuzzleSolution.SOLVABLE
 import kotlin.random.Random
 
 fun generateGame(size: Int = 6): Game {
@@ -68,24 +70,33 @@ internal fun solve(
     if (grid.cells.all { it.selection != null }) return SOLVABLE
 
     // If there are still cells with multiple items, pick one and try each item in turn, then go back to step 2.
-    for (i in 0 until grid.size) {
+    return if (
-        for (j in 0 until grid.size) {
+        grid.cells
-            val cell = grid[i][j]
+            .filter { it.selection == null }
-            if (cell.selection == null) {
+            .any { it.countSolutions(grid, clues) == 1 }
-                val options = cell.options.toList()
+    ) {
+        SOLVABLE
+    } else {
+        MULTIPLE_SOLUTIONS
+    }
+}
+
+internal fun <C : ItemClass<C>> GameCell<C>.countSolutions(
+    grid: Grid,
+    clues: Collection<Clue>
+): Int {
+    val options = options.toList()
+    var solvableCount = 0
     for (option in options) {
-                    cell.selection = option
+        selection = option
         if (solve(grid, clues) == SOLVABLE) {
-                        return SOLVABLE
+            solvableCount++
         }
     }
-                cell.selection = null
+    selection = null
-                cell.options.addAll(options)
+    this.options.addAll(options)
-            }
+
-        }
+    return solvableCount
-    }
-    // This shouldn't happen, as we don't check if there are more solutions once we find one
-    return MULTIPLE_SOLUTIONS
 }
 
 internal enum class PuzzleSolution {