Welcome to your daily brain workout! This puzzle famously stumped mathematicians when it first appeared. Even Nobel Prize winners got it wrong. Can you get it right?

🧩 Today’s Puzzle: The Monty Hall Problem

You’re on a game show. There are three doors. Behind one door is a car; behind the other two, goats. You pick Door #1. The host (who knows what’s behind each door) opens Door #3, revealing a goat. He then asks: “Do you want to switch to Door #2?”

Should you switch? Does it matter? And what are your odds of winning the car if you switch vs. if you stay?

💡 Hint

Your initial odds of picking the car were 1/3. The host opening a door doesn’t change what was behind your original door. Think about it: if you initially picked a goat (2/3 chance), switching gets you the car. If you initially picked the car (1/3 chance), switching gets you a goat.

📅 Yesterday’s Answer (June 22)

Puzzle: The Blue-Eyed Islanders — 100 people with blue eyes, 100 with brown eyes. A visitor says “I see at least one person with blue eyes.” Who leaves and when?

✅ Answer: All 100 blue-eyed people leave on the 100th midnight. By induction: if only 1 person had blue eyes, they’d leave night 1 (seeing no other blue eyes). With 2, each sees 1 blue-eyed person — when they don’t leave night 1, both realize they must be the second. This chain reaction continues through all 100. The visitor’s statement creates “common knowledge.”

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