Add explanation for inconsistency

Add an "Explain" button next to "Reset" in the Knights and Knaves puzzle. When clicked, this button displays an explanation for any inconsistencies found in the arena below it.

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">
@@ -145,11 +193,19 @@ 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>
+                <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 ? (
                 <p className="text-muted-foreground text-sm">
@@ -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>