689 lines
26 KiB
TypeScript
689 lines
26 KiB
TypeScript
import React, { useState, useEffect, useRef, useCallback } from 'react';
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import { Button } from '@/components/ui/button';
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import { Slider } from '@/components/ui/slider';
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import { Card, CardContent, CardHeader, CardTitle } from '@/components/ui/card';
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import { Badge } from '@/components/ui/badge';
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import { Dialog, DialogContent, DialogHeader, DialogTitle, DialogTrigger } from '@/components/ui/dialog';
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import { Tabs, TabsContent, TabsList, TabsTrigger } from '@/components/ui/tabs';
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import { Play, Pause, RotateCcw, SkipForward, FastForward, Info, ExternalLink, BarChart3 } from 'lucide-react';
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import { BarChart, Bar, XAxis, YAxis, CartesianGrid, Tooltip, ResponsiveContainer, ReferenceLine, Cell } from 'recharts';
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import SocialShare from '@/components/SocialShare';
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interface LadybugClockPuzzleProps {
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showSocialShare?: boolean;
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}
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interface SimulationState {
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position: number; // 0-11 (0 = 12 o'clock, 1 = 1 o'clock, etc.)
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visited: Set<number>;
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path: number[];
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lastPainted: number | null;
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isComplete: boolean;
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moveCount: number;
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}
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const CLOCK_NUMBERS = [12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11];
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const LadybugClockPuzzle: React.FC<LadybugClockPuzzleProps> = ({ showSocialShare = true }) => {
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// Simulation state
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const [simulation, setSimulation] = useState<SimulationState>({
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position: 0,
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visited: new Set([0]),
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path: [0],
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lastPainted: null,
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isComplete: false,
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moveCount: 0
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});
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// Controls
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const [isPlaying, setIsPlaying] = useState(false);
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const [speed, setSpeed] = useState(50); // 1-100, maps to delay
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const [numPositions, setNumPositions] = useState(12);
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// Statistics
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const [lastPaintedCounts, setLastPaintedCounts] = useState<Record<number, number>>({});
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const [totalSimulations, setTotalSimulations] = useState(0);
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const [averageMoves, setAverageMoves] = useState(0);
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const [totalMoves, setTotalMoves] = useState(0);
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// User prediction
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const [userPrediction, setUserPrediction] = useState<number | null>(null);
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const [showPredictionResult, setShowPredictionResult] = useState(false);
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// Refs
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const animationRef = useRef<number | null>(null);
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const isPlayingRef = useRef(isPlaying);
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useEffect(() => {
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isPlayingRef.current = isPlaying;
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}, [isPlaying]);
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// Get delay from speed (inverse relationship)
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const getDelay = useCallback(() => {
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return Math.max(50, 1000 - (speed * 9));
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}, [speed]);
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// Reset simulation
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const resetSimulation = useCallback(() => {
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setIsPlaying(false);
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if (animationRef.current) {
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cancelAnimationFrame(animationRef.current);
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}
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setSimulation({
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position: 0,
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visited: new Set([0]),
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path: [0],
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lastPainted: null,
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isComplete: false,
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moveCount: 0
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});
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}, []);
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// Perform one step
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const step = useCallback(() => {
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setSimulation(prev => {
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if (prev.isComplete) return prev;
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// Random move: clockwise or counterclockwise
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const direction = Math.random() < 0.5 ? 1 : -1;
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const newPosition = ((prev.position + direction) % numPositions + numPositions) % numPositions;
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const newVisited = new Set(prev.visited);
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const wasNewlyPainted = !newVisited.has(newPosition);
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newVisited.add(newPosition);
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const isNowComplete = newVisited.size === numPositions;
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const lastPainted = isNowComplete && wasNewlyPainted ? newPosition : prev.lastPainted;
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return {
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position: newPosition,
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visited: newVisited,
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path: [...prev.path, newPosition],
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lastPainted: lastPainted,
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isComplete: isNowComplete,
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moveCount: prev.moveCount + 1
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};
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});
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}, [numPositions]);
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// Auto-play loop
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useEffect(() => {
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if (!isPlaying || simulation.isComplete) {
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return;
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}
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const timeoutId = setTimeout(() => {
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if (isPlayingRef.current && !simulation.isComplete) {
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step();
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}
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}, getDelay());
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return () => clearTimeout(timeoutId);
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}, [isPlaying, simulation, step, getDelay]);
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// Handle simulation completion
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useEffect(() => {
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if (simulation.isComplete && simulation.lastPainted !== null) {
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setIsPlaying(false);
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}
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}, [simulation.isComplete, simulation.lastPainted]);
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// Run instant simulation (no animation)
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const runInstantSimulation = useCallback(() => {
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let position = 0;
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const visited = new Set([0]);
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let moveCount = 0;
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let lastPainted = 0;
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while (visited.size < numPositions) {
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const direction = Math.random() < 0.5 ? 1 : -1;
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position = ((position + direction) % numPositions + numPositions) % numPositions;
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if (!visited.has(position)) {
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lastPainted = position;
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visited.add(position);
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}
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moveCount++;
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}
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return { lastPainted, moveCount };
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}, [numPositions]);
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// Run to completion
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const runToCompletion = useCallback(() => {
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setIsPlaying(false);
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let currentSim = simulation;
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let position = currentSim.position;
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const visited = new Set(currentSim.visited);
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let moveCount = currentSim.moveCount;
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let lastPainted = currentSim.lastPainted;
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const path = [...currentSim.path];
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while (visited.size < numPositions) {
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const direction = Math.random() < 0.5 ? 1 : -1;
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position = ((position + direction) % numPositions + numPositions) % numPositions;
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path.push(position);
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if (!visited.has(position)) {
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lastPainted = position;
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visited.add(position);
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}
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moveCount++;
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}
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setSimulation({
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position,
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visited,
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path,
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lastPainted,
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isComplete: true,
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moveCount
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});
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}, [simulation, numPositions]);
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// Run batch simulations
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const runBatchSimulations = useCallback((count: number) => {
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const newCounts = { ...lastPaintedCounts };
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let batchMoves = 0;
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for (let i = 0; i < count; i++) {
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const result = runInstantSimulation();
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newCounts[result.lastPainted] = (newCounts[result.lastPainted] || 0) + 1;
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batchMoves += result.moveCount;
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}
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setLastPaintedCounts(newCounts);
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setTotalSimulations(prev => prev + count);
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setTotalMoves(prev => prev + batchMoves);
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setAverageMoves((totalMoves + batchMoves) / (totalSimulations + count));
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}, [lastPaintedCounts, runInstantSimulation, totalMoves, totalSimulations]);
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// Clear statistics
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const clearStats = useCallback(() => {
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setLastPaintedCounts({});
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setTotalSimulations(0);
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setAverageMoves(0);
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setTotalMoves(0);
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setUserPrediction(null);
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setShowPredictionResult(false);
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}, []);
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// Reset everything when numPositions changes
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useEffect(() => {
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resetSimulation();
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clearStats();
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}, [numPositions, resetSimulation, clearStats]);
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// Convert position index to display number
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const positionToNumber = (pos: number) => {
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if (numPositions === 12) {
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return pos === 0 ? 12 : pos;
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}
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return pos + 1;
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};
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// Calculate clock position for a given index
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const getClockPosition = (index: number, radius: number) => {
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const angle = (index / numPositions) * 2 * Math.PI - Math.PI / 2;
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return {
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x: Math.cos(angle) * radius,
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y: Math.sin(angle) * radius
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};
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};
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// Prepare chart data
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const chartData = Array.from({ length: numPositions - 1 }, (_, i) => {
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const pos = i + 1; // 1 to n-1 (0/12 can't be last)
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const count = lastPaintedCounts[pos] || 0;
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const percentage = totalSimulations > 0 ? (count / totalSimulations) * 100 : 0;
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return {
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position: positionToNumber(pos),
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count,
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percentage,
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label: `${positionToNumber(pos)}`
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};
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});
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const theoreticalProbability = 100 / (numPositions - 1);
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const shareUrl = typeof window !== 'undefined'
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? `${window.location.origin}/puzzles/ladybug-clock`
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: '';
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return (
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<div className="w-full max-w-6xl mx-auto px-4 space-y-6">
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{/* Header */}
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<div className="text-center space-y-2">
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<h1 className="text-3xl font-bold text-foreground">The Ladybug Clock Puzzle</h1>
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<p className="text-muted-foreground max-w-2xl mx-auto">
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A ladybug walks randomly on a clock face. What's the probability each number is painted last?
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</p>
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</div>
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<div className="grid lg:grid-cols-2 gap-6">
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{/* Clock Visualization */}
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<Card className="bg-[#1a1a2e] border-slate-700">
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<CardContent className="p-6">
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<div className="relative w-full aspect-square max-w-md mx-auto">
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<svg viewBox="-150 -150 300 300" className="w-full h-full">
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{/* Clock face background */}
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<circle cx="0" cy="0" r="140" fill="#2d2d44" stroke="#4a4a6a" strokeWidth="3" />
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<circle cx="0" cy="0" r="120" fill="none" stroke="#3d3d5c" strokeWidth="1" strokeDasharray="4 4" />
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{/* Hour markers and numbers */}
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{Array.from({ length: numPositions }, (_, i) => {
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const pos = getClockPosition(i, 100);
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const isPainted = simulation.visited.has(i);
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const isLast = simulation.isComplete && simulation.lastPainted === i;
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const isCurrent = simulation.position === i;
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return (
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<g key={i}>
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{/* Tick mark */}
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<line
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x1={getClockPosition(i, 115).x}
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y1={getClockPosition(i, 115).y}
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x2={getClockPosition(i, 125).x}
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y2={getClockPosition(i, 125).y}
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stroke={isPainted ? '#f59e0b' : '#6b7280'}
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strokeWidth="2"
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/>
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{/* Number circle background */}
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<circle
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cx={pos.x}
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cy={pos.y}
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r="20"
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fill={isLast ? '#ef4444' : isPainted ? '#f59e0b' : '#374151'}
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className="transition-all duration-300"
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/>
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{/* Glow effect for newly painted or last */}
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{(isPainted || isLast) && (
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<circle
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cx={pos.x}
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cy={pos.y}
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r="24"
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fill="none"
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stroke={isLast ? '#ef4444' : '#f59e0b'}
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strokeWidth="2"
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opacity="0.5"
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/>
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)}
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{/* Number text */}
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<text
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x={pos.x}
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y={pos.y}
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textAnchor="middle"
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dominantBaseline="central"
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fill={isPainted ? '#1a1a2e' : '#d1d5db'}
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fontSize="14"
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fontWeight="bold"
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className="select-none"
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>
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{positionToNumber(i)}
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</text>
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</g>
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);
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})}
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{/* Ladybug */}
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{(() => {
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const ladybugPos = getClockPosition(simulation.position, 100);
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return (
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<g
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transform={`translate(${ladybugPos.x}, ${ladybugPos.y})`}
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className="transition-transform duration-200"
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>
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{/* Ladybug body */}
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<ellipse cx="0" cy="-30" rx="12" ry="15" fill="#dc2626" />
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{/* Head */}
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<circle cx="0" cy="-48" r="6" fill="#1f2937" />
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{/* Center line */}
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<line x1="0" y1="-45" x2="0" y2="-15" stroke="#1f2937" strokeWidth="2" />
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{/* Spots */}
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<circle cx="-5" cy="-35" r="3" fill="#1f2937" />
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<circle cx="5" cy="-35" r="3" fill="#1f2937" />
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<circle cx="-4" cy="-24" r="2.5" fill="#1f2937" />
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<circle cx="4" cy="-24" r="2.5" fill="#1f2937" />
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{/* Antennae */}
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<line x1="-3" y1="-52" x2="-6" y2="-58" stroke="#1f2937" strokeWidth="1.5" />
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<line x1="3" y1="-52" x2="6" y2="-58" stroke="#1f2937" strokeWidth="1.5" />
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</g>
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);
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})()}
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{/* Center decoration */}
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<circle cx="0" cy="0" r="8" fill="#4a4a6a" />
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</svg>
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</div>
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{/* Status display */}
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<div className="mt-4 text-center space-y-2">
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<div className="flex justify-center gap-4 text-sm">
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<Badge variant="outline" className="bg-slate-800 text-slate-200">
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Position: {positionToNumber(simulation.position)}
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</Badge>
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<Badge variant="outline" className="bg-slate-800 text-slate-200">
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Moves: {simulation.moveCount}
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</Badge>
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<Badge variant="outline" className="bg-slate-800 text-slate-200">
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Painted: {simulation.visited.size}/{numPositions}
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</Badge>
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</div>
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{simulation.isComplete && simulation.lastPainted !== null && (
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<div className="p-3 bg-red-500/20 border border-red-500/50 rounded-lg">
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<p className="text-red-400 font-semibold">
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🎉 Complete! Last painted: <span className="text-red-300 text-lg">{positionToNumber(simulation.lastPainted)}</span>
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</p>
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</div>
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)}
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</div>
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</CardContent>
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</Card>
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{/* Controls and Stats */}
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<div className="space-y-4">
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{/* Simulation Controls */}
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<Card>
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<CardHeader className="pb-3">
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<CardTitle className="text-lg">Simulation Controls</CardTitle>
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</CardHeader>
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<CardContent className="space-y-4">
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<div className="flex flex-wrap gap-2">
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<Button
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onClick={() => setIsPlaying(!isPlaying)}
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disabled={simulation.isComplete}
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variant={isPlaying ? "destructive" : "default"}
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size="sm"
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>
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{isPlaying ? <Pause className="w-4 h-4 mr-1" /> : <Play className="w-4 h-4 mr-1" />}
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{isPlaying ? 'Pause' : 'Play'}
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</Button>
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<Button
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onClick={step}
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disabled={simulation.isComplete || isPlaying}
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variant="outline"
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size="sm"
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>
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<SkipForward className="w-4 h-4 mr-1" />
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Step
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</Button>
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<Button
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onClick={runToCompletion}
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disabled={simulation.isComplete}
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variant="outline"
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size="sm"
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>
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<FastForward className="w-4 h-4 mr-1" />
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Complete
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</Button>
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<Button onClick={resetSimulation} variant="outline" size="sm">
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<RotateCcw className="w-4 h-4 mr-1" />
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Reset
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</Button>
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</div>
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<div className="space-y-2">
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<label className="text-sm text-muted-foreground">Animation Speed</label>
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<Slider
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value={[speed]}
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onValueChange={(v) => setSpeed(v[0])}
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min={1}
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max={100}
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step={1}
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className="w-full"
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/>
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</div>
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<div className="space-y-2">
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<label className="text-sm text-muted-foreground">Number of Positions: {numPositions}</label>
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<Slider
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value={[numPositions]}
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onValueChange={(v) => setNumPositions(v[0])}
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min={4}
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max={24}
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step={2}
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className="w-full"
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/>
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</div>
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</CardContent>
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</Card>
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{/* Batch Simulations */}
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<Card>
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<CardHeader className="pb-3">
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<CardTitle className="text-lg flex items-center gap-2">
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<BarChart3 className="w-5 h-5" />
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Batch Simulations
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</CardTitle>
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</CardHeader>
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<CardContent className="space-y-4">
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<div className="flex flex-wrap gap-2">
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{[100, 1000, 10000].map(count => (
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<Button
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key={count}
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onClick={() => runBatchSimulations(count)}
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variant="outline"
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size="sm"
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>
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Run {count.toLocaleString()}
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</Button>
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))}
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<Button onClick={clearStats} variant="ghost" size="sm">
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Clear Stats
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</Button>
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</div>
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<div className="text-sm space-y-1">
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<p className="text-muted-foreground">
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Total simulations: <span className="text-foreground font-medium">{totalSimulations.toLocaleString()}</span>
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</p>
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{totalSimulations > 0 && (
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<p className="text-muted-foreground">
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Average moves to complete: <span className="text-foreground font-medium">{averageMoves.toFixed(1)}</span>
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</p>
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)}
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</div>
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</CardContent>
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</Card>
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{/* User Prediction */}
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{totalSimulations === 0 && (
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<Card className="border-primary/50 bg-primary/5">
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<CardHeader className="pb-3">
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<CardTitle className="text-lg">Make a Prediction! 🤔</CardTitle>
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</CardHeader>
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<CardContent>
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<p className="text-sm text-muted-foreground mb-3">
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Which number do you think is most likely to be painted last?
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</p>
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<div className="flex flex-wrap gap-2">
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{Array.from({ length: numPositions - 1 }, (_, i) => i + 1).map(pos => (
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<Button
|
|
key={pos}
|
|
onClick={() => setUserPrediction(pos)}
|
|
variant={userPrediction === pos ? "default" : "outline"}
|
|
size="sm"
|
|
className="w-10 h-10"
|
|
>
|
|
{positionToNumber(pos)}
|
|
</Button>
|
|
))}
|
|
</div>
|
|
{userPrediction !== null && (
|
|
<p className="mt-3 text-sm text-primary">
|
|
You predicted: <strong>{positionToNumber(userPrediction)}</strong>. Run some simulations to see!
|
|
</p>
|
|
)}
|
|
</CardContent>
|
|
</Card>
|
|
)}
|
|
</div>
|
|
</div>
|
|
|
|
{/* Statistics Chart */}
|
|
{totalSimulations > 0 && (
|
|
<Card>
|
|
<CardHeader>
|
|
<CardTitle className="flex items-center gap-2">
|
|
Statistics: Which number was painted last?
|
|
<Badge variant="secondary">{totalSimulations.toLocaleString()} simulations</Badge>
|
|
</CardTitle>
|
|
</CardHeader>
|
|
<CardContent>
|
|
<div className="h-64">
|
|
<ResponsiveContainer width="100%" height="100%">
|
|
<BarChart data={chartData} margin={{ top: 20, right: 30, left: 20, bottom: 5 }}>
|
|
<CartesianGrid strokeDasharray="3 3" stroke="#374151" />
|
|
<XAxis dataKey="label" stroke="#9ca3af" />
|
|
<YAxis
|
|
stroke="#9ca3af"
|
|
tickFormatter={(v) => `${v.toFixed(1)}%`}
|
|
domain={[0, Math.max(theoreticalProbability * 1.5, 15)]}
|
|
/>
|
|
<Tooltip
|
|
contentStyle={{ backgroundColor: '#1f2937', border: '1px solid #374151' }}
|
|
labelStyle={{ color: '#f3f4f6' }}
|
|
formatter={(value: number) => [`${value.toFixed(2)}%`, 'Probability']}
|
|
/>
|
|
<ReferenceLine
|
|
y={theoreticalProbability}
|
|
stroke="#22c55e"
|
|
strokeDasharray="5 5"
|
|
label={{
|
|
value: `Theory: ${theoreticalProbability.toFixed(2)}%`,
|
|
fill: '#22c55e',
|
|
fontSize: 12,
|
|
position: 'right'
|
|
}}
|
|
/>
|
|
<Bar dataKey="percentage" radius={[4, 4, 0, 0]}>
|
|
{chartData.map((entry, index) => (
|
|
<Cell
|
|
key={`cell-${index}`}
|
|
fill={userPrediction === index + 1 ? '#8b5cf6' : '#f59e0b'}
|
|
/>
|
|
))}
|
|
</Bar>
|
|
</BarChart>
|
|
</ResponsiveContainer>
|
|
</div>
|
|
|
|
{userPrediction !== null && (
|
|
<div className="mt-4 p-3 bg-purple-500/10 border border-purple-500/30 rounded-lg">
|
|
<p className="text-sm">
|
|
<strong className="text-purple-400">Your prediction ({positionToNumber(userPrediction)}):</strong>{' '}
|
|
{((lastPaintedCounts[userPrediction] || 0) / totalSimulations * 100).toFixed(2)}%
|
|
{' '}— Theory predicts all numbers have equal probability of{' '}
|
|
<span className="text-green-400">{theoreticalProbability.toFixed(2)}%</span>!
|
|
</p>
|
|
</div>
|
|
)}
|
|
|
|
<div className="mt-4 p-3 bg-amber-500/10 border border-amber-500/30 rounded-lg">
|
|
<p className="text-sm text-amber-200">
|
|
<strong>The Surprising Result:</strong> Despite {numPositions === 12 ? '6' : Math.floor(numPositions / 2)} being the farthest from the start,
|
|
every number (1-{numPositions - 1}) has an equal probability of being painted last: exactly 1/{numPositions - 1} ≈ {theoreticalProbability.toFixed(2)}%!
|
|
</p>
|
|
</div>
|
|
</CardContent>
|
|
</Card>
|
|
)}
|
|
|
|
{/* Path History */}
|
|
{simulation.path.length > 1 && (
|
|
<Card>
|
|
<CardHeader className="pb-3">
|
|
<CardTitle className="text-lg">Path History</CardTitle>
|
|
</CardHeader>
|
|
<CardContent>
|
|
<div className="flex flex-wrap gap-1 max-h-32 overflow-y-auto">
|
|
{simulation.path.map((pos, i) => (
|
|
<Badge
|
|
key={i}
|
|
variant={i === 0 ? "default" : "outline"}
|
|
className={`${
|
|
simulation.isComplete && i === simulation.path.length - 1
|
|
? 'bg-red-500 text-white'
|
|
: ''
|
|
}`}
|
|
>
|
|
{positionToNumber(pos)}
|
|
</Badge>
|
|
))}
|
|
</div>
|
|
</CardContent>
|
|
</Card>
|
|
)}
|
|
|
|
{/* Educational Info */}
|
|
<Card>
|
|
<CardHeader>
|
|
<CardTitle className="flex items-center gap-2">
|
|
<Info className="w-5 h-5" />
|
|
About This Puzzle
|
|
</CardTitle>
|
|
</CardHeader>
|
|
<CardContent className="space-y-4">
|
|
<div className="prose prose-sm dark:prose-invert max-w-none">
|
|
<h4 className="text-foreground">The Rules</h4>
|
|
<ul className="text-muted-foreground">
|
|
<li>A ladybug starts at the 12 o'clock position</li>
|
|
<li>Each second, it randomly moves one step clockwise or counterclockwise (50/50 chance)</li>
|
|
<li>When the ladybug visits a number, that number gets "painted"</li>
|
|
<li>The simulation ends when all numbers have been visited at least once</li>
|
|
</ul>
|
|
|
|
<h4 className="text-foreground">The Surprising Result</h4>
|
|
<p className="text-muted-foreground">
|
|
Intuitively, you might expect the number 6 (opposite to 12) to be the most likely to be painted last,
|
|
since it's the farthest from the starting point. However, the probability is exactly <strong>1/{numPositions - 1}</strong> for
|
|
every number from 1 to {numPositions - 1}! This is because once all but one number is painted, the random walk
|
|
will eventually reach that last number, regardless of where it is.
|
|
</p>
|
|
|
|
<h4 className="text-foreground">Mathematical Connections</h4>
|
|
<ul className="text-muted-foreground">
|
|
<li><strong>Random Walks on Cycles:</strong> This is an example of a random walk on a cycle graph</li>
|
|
<li><strong>Cover Time:</strong> The number of moves to visit all vertices is called the "cover time"</li>
|
|
<li><strong>Gambler's Ruin:</strong> Related to the classic probability problem of a gambler with a finite amount</li>
|
|
</ul>
|
|
</div>
|
|
</CardContent>
|
|
</Card>
|
|
|
|
{/* Acknowledgement */}
|
|
<Card className="bg-amber-50 dark:bg-amber-950/30 border-amber-200 dark:border-amber-800">
|
|
<CardContent className="pt-6">
|
|
<p className="text-sm text-muted-foreground">
|
|
This puzzle is featured by{' '}
|
|
<a href="https://momath.org/mindbenders/" target="_blank" rel="noopener noreferrer" className="text-primary hover:underline font-medium">
|
|
MoMath Mindbenders
|
|
</a>
|
|
{' '}and demonstrated in{' '}
|
|
<a href="https://www.youtube.com/shorts/t3jZ2xGOvYg" target="_blank" rel="noopener noreferrer" className="text-primary hover:underline font-medium">
|
|
this YouTube short
|
|
</a>.
|
|
</p>
|
|
</CardContent>
|
|
</Card>
|
|
|
|
{showSocialShare && (
|
|
<SocialShare
|
|
title="The Ladybug Clock Puzzle"
|
|
description="Explore random walks on a clock face and discover why every number has the same probability of being painted last!"
|
|
url={shareUrl}
|
|
/>
|
|
)}
|
|
</div>
|
|
);
|
|
};
|
|
|
|
export default LadybugClockPuzzle;
|