Logic problem 9 of 30

Guess the number

Logic
Easy

I am thinking of a whole number from 1 to 1000. After each guess I tell you "higher", "lower" or "correct".

With the best strategy, what is the maximum number of guesses you could need?

Show hint

Each guess should cut the remaining range in half. How many times can you halve 1000 before only one number is left?

Show solution

10 guesses.

With k guesses, binary search can tell apart at most 2^k − 1 numbers. 2⁹ − 1 = 511 is too few, while 2¹⁰ − 1 = 1023 covers all 1000. This is why binary search is O(log n).

Want a problem like this every day? See today's problem and keep a streak going.