diff --git a/src/components/KnightsAndKnavesI.tsx b/src/components/KnightsAndKnavesI.tsx
index 41882cd..e7e5153 100644
--- a/src/components/KnightsAndKnavesI.tsx
+++ b/src/components/KnightsAndKnavesI.tsx
@@ -15,7 +15,7 @@ type StatementId = typeof STATEMENTS[number]["id"];
 
 const KnightsAndKnavesI = () => {
   const [inArena, setInArena] = useState<StatementId[]>([]);
-
+  const [showExplain, setShowExplain] = useState(false);
   // SEO basics
   useEffect(() => {
     const title = "Knights and Knaves – I (Logic Puzzle)";
@@ -100,6 +100,54 @@ const KnightsAndKnavesI = () => {
     isConsistent ? "bg-surface border-outline" : "bg-destructive/10 border-destructive"
   );
 
+  function generateExplanation(idsArr: StatementId[]): string[] {
+    const ids = new Set(idsArr);
+    const lines: string[] = [];
+
+    // Direct role contradictions
+    if (ids.has("AK") && ids.has("AN")) lines.push("A cannot be both a knight and a knave.");
+    if (ids.has("BK") && ids.has("BN")) lines.push("B cannot be both a knight and a knave.");
+
+    // A's utterance linkage
+    if (ids.has("S")) {
+      const forcedA = ids.has("AK") ? true : ids.has("AN") ? false : null;
+      const forcedB = ids.has("BK") ? true : ids.has("BN") ? false : null;
+
+      if (forcedA === true && forcedB === true) {
+        lines.push("If A and B are both knights, then A’s statement “at least one of us is a knave” is false; but a knight cannot assert a falsehood.");
+      }
+      if (forcedA === false) {
+        lines.push("If A is a knave, his statement must be false. “At least one of us is a knave” being false means neither is a knave (both are knights), contradicting “A is a knave” and any claim that B is a knave.");
+      }
+      if (forcedB === true && forcedA === null) {
+        lines.push("B is a knight. If A were a knight, his statement would be false; if A were a knave, his statement would be true. Either way, A’s truthfulness would not match his statement, so no assignment works.");
+      }
+
+      // Enumerate remaining candidate assignments for clarity
+      if (lines.length === 0) {
+        const aVals = forcedA === null ? [true, false] : [forcedA];
+        const bVals = forcedB === null ? [true, false] : [forcedB];
+        for (const aKnight of aVals) {
+          for (const bKnight of bVals) {
+            const content = (!aKnight) || (!bKnight);
+            const ok = (aKnight === content);
+            if (!ok) {
+              const contentTruth = content ? "true" : "false";
+              lines.push(`If A is ${aKnight ? "a knight" : "a knave"} and B is ${bKnight ? "a knight" : "a knave"}, then the content “at least one of us is a knave” is ${contentTruth}, which a ${aKnight ? "knight must tell" : "knave must not tell"}.`);
+            }
+          }
+        }
+      }
+    }
+
+    if (lines.length === 0) lines.push("The selected set cannot be satisfied by any assignment of A and B.");
+    return lines;
+  }
+
+  const explanation = useMemo(() => (isConsistent ? [] : generateExplanation(inArena)), [inArena, isConsistent]);
+
+  useEffect(() => { if (isConsistent) setShowExplain(false); }, [isConsistent]);
+
   return (
     <section className="space-y-6">
       <header className="space-y-2">
@@ -145,10 +193,18 @@ const KnightsAndKnavesI = () => {
               <div className="flex items-center justify-between mb-4">
                 <p className={cn("text-sm font-medium", isConsistent ? "text-success" : "text-destructive")}
                 >{isConsistent ? "Consistent" : "Incompatible set"}</p>
-                <button
-                  onClick={reset}
-                  className="text-muted-foreground hover:text-foreground text-sm"
-                >Reset</button>
+                <div className="flex items-center gap-3">
+                  {!isConsistent && (
+                    <button
+                      onClick={() => setShowExplain((v) => !v)}
+                      className="text-destructive hover:text-destructive/80 text-sm"
+                    >Explain</button>
+                  )}
+                  <button
+                    onClick={reset}
+                    className="text-muted-foreground hover:text-foreground text-sm"
+                  >Reset</button>
+                </div>
               </div>
 
               {inArena.length === 0 ? (
@@ -179,6 +235,16 @@ const KnightsAndKnavesI = () => {
               )}
             </div>
           </div>
+          {showExplain && !isConsistent && (
+            <div className="mt-4 rounded-md border border-outline bg-surface p-4">
+              <h2 className="text-sm font-semibold mb-2">Why inconsistent?</h2>
+              <ul className="list-disc pl-5 space-y-1 text-sm text-foreground">
+                {explanation.map((line, i) => (
+                  <li key={i}>{line}</li>
+                ))}
+              </ul>
+            </div>
+          )}
         </div>
       </div>
     </section>