So, let’s say the number you were trying to guess is a ‘1’. Then, you would start from the middle of 1,000 – which is 500. The person giving you hints would keep saying lower – and you would end up with something like this sequence of numbers to represent your guesses: 500, 250, 125, 63, 32, 16, 8, 4, 2, 1 Counting the number of guesses above would give you 10, which is our answer to the maximum number of guesses to find a number between 1 and 1000. In a binary search, if you take the log base 2 of the number of numbers (in this case, 1000), that would also give you the maximum number of guesses to find the correct number. So, if we take the log base 2 of 1,000 it would give us 9.965. Since you can’t possibly have a fraction of a guess, the result of log base 2 of 1000 should be rounded up to a whole number, which is 10, and the answer.