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1. Number Logic
Question. What is the next number in the sequence: 2, 6, 12, 20, 30, ...?
Explanation: The differences are 4, 6, 8, 10, so the next difference is 12 → 30 + 12 = 42.
Answer. 42
2. Probability Calculation (Beat The Odds)
Question. You have a 60% chance of winning each play. If you play 3 times, what is the probability of exactly 2 wins?
Explanation: A binomial probability problem. P(X=2) = C(3,2) - (0.6)² - (0.4)¹ = 3-0.36-0.4 = 0.432
Answer. 0.432 (43.2%)
3. Programming Question
Question. Write a Python function to check if a string is a palindrome.
def is_palindrome(s: str) → bool.
return s == s[::-1]
# Examples
print(is_palindrome("racecar")) # True
print(is_palindrome("hello")) # False
4. Short-term Brain Game (Hat Puzzle)
Question. 100 people stand in line each wearing a red or blue hat. They can see others' hats but not their own and must guess simultaneously. What strategy maximizes correct guesses?
Answer. Use parity of blue hats: The first person declares "blue" if they see an odd number of blue hats, "red" if even. "Each subsequent person deduces their own hat color from the changing parity, ensuring at least 99 correct guesses.
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