diff --git a/commonUI/src/commonMain/kotlin/ch/dissem/yaep/ui/common/App.kt b/commonUI/src/commonMain/kotlin/ch/dissem/yaep/ui/common/App.kt
index 99f245b..3ee222f 100644
--- a/commonUI/src/commonMain/kotlin/ch/dissem/yaep/ui/common/App.kt
+++ b/commonUI/src/commonMain/kotlin/ch/dissem/yaep/ui/common/App.kt
@@ -127,10 +127,8 @@ fun PuzzleGrid(
                         allOptions.map { Toggleable(it, item.options.contains(it)) }
                     }
                     LaunchedEffect(item) {
-                        item.optionsRemovedListeners.add { removed ->
-                            options
-                                .filter { removed.contains(it.item) }
-                                .forEach { it.enabled = false }
+                        item.optionsChangedListeners.add { enabled ->
+                            options.forEach { it.enabled = enabled.contains(it.item) }
                         }
                         item.selectionChangedListeners.add {
                             selection = it
@@ -151,9 +149,17 @@ fun PuzzleGrid(
                         },
                         selectedItem = selection,
                         onSelectItem = {
-                            item.selection = it
                             if (it != null) {
+                                grid.snapshot()
+                                item.selection = it
                                 row.cleanupOptions()
+                            } else {
+                                while (item.selection != null) {
+                                    if (!grid.undo()) break
+                                }
+                                options.forEach {
+                                    it.enabled = item.options.contains(it.item)
+                                }
                             }
                         }
                     )
diff --git a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Game.kt b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Game.kt
index 6db2ef5..f309ca1 100644
--- a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Game.kt
+++ b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Game.kt
@@ -16,6 +16,7 @@ class Game(
             row.forEachIndexed { index, gameCell ->
                 if (index == position.index) {
                     gameCell.selection = position.item
+                    gameCell.mutable = false
                 } else {
                     gameCell.options.remove(position.item)
                 }
@@ -23,7 +24,7 @@ class Game(
         }
         grid.forEach { row ->
             row.forEach { cell ->
-                cell.optionsRemovedListeners.add {
+                cell.optionsChangedListeners.add {
                     if (onStartListeners.isNotEmpty()) {
                         onStartListeners.forEach { it() }
                         onStartListeners.clear()
diff --git a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameCell.kt b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameCell.kt
index 9e2f723..0c5e842 100644
--- a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameCell.kt
+++ b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameCell.kt
@@ -1,19 +1,43 @@
 package ch.dissem.yaep.domain
 
 class GameCell<C : ItemClass<C>>(
-    selection: Item<C>?=null,
+    selection: Item<C>? = null,
     val solution: Item<C>? = null,
-    options: Collection<Item<C>>
+    options: Collection<Item<C>>,
+    /*** If mutable is false, the cell will silently ignore all changes to 'selection'. */
+    var mutable: Boolean = true
 ) {
-    val selectionChangedListeners = mutableListOf<(Item<C>?) -> Unit>()
-    val optionsRemovedListeners = mutableListOf<(Collection<Item<C>>) -> Unit>()
+    val selectionChangedListeners: MutableList<(Item<C>?) -> Unit> =
+        mutableListOf<(Item<C>?) -> Unit>()
+    val optionsChangedListeners: MutableList<(Collection<Item<C>>) -> Unit> =
+        mutableListOf<(Collection<Item<C>>) -> Unit>()
 
     var selection: Item<C>? = selection
         set(value) {
-            field = value
-            selectionChangedListeners.forEach { listener -> listener(value) }
+            if (mutable) {
+                field = value
+                selectionChangedListeners.forEach { listener -> listener(value) }
+            }
         }
-    val options = ObservableSet(options.toMutableSet()) { optionsRemovedListeners.forEach { listener -> listener(it) } }
+    val options: ObservableSet<Item<C>> = ObservableSet(options.toMutableSet()) { before, after ->
+        optionsChangedListeners.forEach { listener ->
+            listener(after)
+        }
+    }
+
+    private val snapshots = ArrayDeque<Pair<Item<C>?, Collection<Item<C>>>>()
+
+    fun snapshot() {
+        snapshots.addLast(selection to options.toSet())
+    }
+
+    fun undo(): Boolean {
+        val (selection, options) = snapshots.removeLastOrNull() ?: return false
+        this.selection = selection
+        this.options.clear()
+        this.options.addAll(options)
+        return true
+    }
 }
 
 fun <C : ItemClass<C>> GameCell<C>?.mayBe(item: Item<C>, mayHaveSelection: Boolean = true) =
@@ -23,5 +47,5 @@ fun <C : ItemClass<C>> GameCell<C>?.mayBe(item: Item<C>, mayHaveSelection: Boole
 fun <C : ItemClass<C>> GameCell<C>?.isA(item: Item<C>) =
     this != null && selection == item
 
-fun <C : ItemClass<C>> GameCell<C>?.hasNoSelection() = this != null && this.selection == null
+fun <C : ItemClass<C>> GameCell<C>?.hasNoSelection(): Boolean = this != null && this.selection == null
 
diff --git a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameRow.kt b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameRow.kt
index d58a1a1..2bed349 100644
--- a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameRow.kt
+++ b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/GameRow.kt
@@ -5,20 +5,20 @@ class GameRow<C : ItemClass<C>>(
     val options: List<Item<C>>,
     val cells: List<GameCell<C>>
 ) : List<GameCell<C>> by cells {
-    var isSolved = false
+    var isSolved: Boolean = false
         private set(value) {
             field = value
             if (value) {
                 onSolvedListener()
             }
         }
-    var onSolvedListener = {}
+    var onSolvedListener: () -> Unit = {}
 
     fun onSolved(listener: () -> Unit) {
         onSolvedListener = listener
     }
 
-    fun indexOf(element: C) = indexOfFirst { it.selection?.itemType == element }
+    fun indexOf(element: C): Int = indexOfFirst { it.selection?.itemType == element }
 
     fun cleanupOptions() {
         if (isSolved && all {
@@ -64,4 +64,19 @@ class GameRow<C : ItemClass<C>>(
         }
     }
 
+    fun snapshot() {
+        cells.forEach { it.snapshot() }
+    }
+
+    fun undo(): Boolean {
+        val didChange = cells.map { it.undo() }.reduce { a, b -> a || b }
+        if (didChange) {
+            isSolved = all {
+                it.solution != null
+                        && it.options.size == 1
+                        && it.options.single() == it.selection
+            }
+        }
+        return didChange
+    }
 }
diff --git a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Grid.kt b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Grid.kt
index 381a92c..903556f 100644
--- a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Grid.kt
+++ b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/Grid.kt
@@ -31,6 +31,14 @@ class Grid(
     fun cleanupOptions() {
         forEach { row -> row.cleanupOptions() }
     }
+
+    fun snapshot() {
+        forEach { row -> row.snapshot() }
+    }
+
+    fun undo(): Boolean {
+        return map { row -> row.undo() }.reduce { a, b -> a || b }
+    }
 }
 
 fun List<List<Item<ItemClass<*>>>>.toGrid() = Grid(
diff --git a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/ObservableSet.kt b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/ObservableSet.kt
index 101f11e..0c43351 100644
--- a/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/ObservableSet.kt
+++ b/domain/src/commonMain/kotlin/ch/dissem/yaep/domain/ObservableSet.kt
@@ -2,28 +2,62 @@ package ch.dissem.yaep.domain
 
 class ObservableSet<E> private constructor(
     private val mutableSet: MutableSet<E>,
-    private val onElementRemoved: (Set<E>) -> Unit
+    private val onElementChanged: (before: Set<E>, after: Set<E>) -> Unit
 ) : MutableSet<E> by mutableSet {
-    constructor(elements: Collection<E>, onElementRemoved: (Set<E>) -> Unit) : this(
+    constructor(
+        elements: Collection<E>,
+        onElementChanged: (before: Set<E>, after: Set<E>) -> Unit
+    ) : this(
         elements.toMutableSet(),
-        onElementRemoved
+        onElementChanged
     )
 
+    private inner class ObservableIterator(
+        private val delegate: MutableIterator<E>
+    ) : MutableIterator<E> by delegate {
+
+        override fun remove() {
+            val previous = mutableSet.toSet()
+            delegate.remove()
+            onElementChanged(previous, mutableSet.toSet())
+        }
+    }
+
+    override fun iterator(): MutableIterator<E> {
+        return ObservableIterator(mutableSet.iterator())
+    }
+
+    override fun add(element: E): Boolean {
+        return observe(setOf(element)) { mutableSet.add(element) }
+    }
+
+
     override fun remove(element: E): Boolean {
-        return observeRemoval(setOf(element)) { mutableSet.remove(element) }
+        return observe(setOf(element)) { mutableSet.remove(element) }
+    }
+
+    override fun addAll(elements: Collection<E>): Boolean {
+        return observe(elements.toSet()) { mutableSet.addAll(elements) }
     }
 
     override fun removeAll(elements: Collection<E>): Boolean =
-        observeRemoval(elements.toSet(), mutableSet::removeAll)
+        observe(elements.toSet(), mutableSet::removeAll)
 
     override fun retainAll(elements: Collection<E>): Boolean =
-        observeRemoval(elements.toSet(), mutableSet::retainAll)
+        observe(elements.toSet(), mutableSet::retainAll)
 
-    private fun observeRemoval(values: Set<E>, operation: (Set<E>) -> Boolean): Boolean {
-        val removed = operation(values)
-        if (removed) {
-            onElementRemoved(values)
+    override fun clear() {
+        return observe(setOf()) { mutableSet.clear() }
+    }
+
+    private fun <R> observe(values: Set<E>, operation: (Set<E>) -> R): R {
+        val previous = mutableSet.toSet()
+        val result = operation(values)
+        val changed = !(previous.containsAll(mutableSet) && previous.size == mutableSet.size)
+        if (changed) {
+            val new = mutableSet.toSet()
+            onElementChanged(previous, new)
         }
-        return removed
+        return result
     }
 }