Puzzle Challenge: Two historians are playing game, can you find way to win it?

New Delhi: Mathematics and history might be two boring subjects for you at school, but when you combine the two, it is always fun. Maths and history give rise to interesting brain teasing problems and puzzles to sharpen your brain.

Here is a puzzle that will take you into the world of maths and history, but no boring formulas and remembering the dates this time.

Situation:

Two historians were playing a year-guessing game. In the game, one needs to guess a year between 1 and 2000 AD where one historian would think of a date and the other would ask some questions to guess the year the first one is thinking of.

The catch is that these questions could only be answered in one of the given three ways:

1. ‘The year is correct.’
2. ‘That year is too early.’
3. ‘That year is too late.’

The first historian announced that he has thought of a year between 1 to 2000 AD and the second historian went into deep thought to develop a strategy. After thinking for some time, he announced that the year can be guessed correctly within a particular number of guesses.

What you need to answer?

Now, when you know the situation and the conditions, try to answer the following question-

In the worst-case scenario, how many guesses would the second historian need to find the correct year?

Answer:

11 guesses. The number can be guessed by halving the search space after each attempt.

How we cracked the puzzle?

The second historian should always start by guessing ‘1000’ or ‘1001’. After the first historian will give one of the given three replies, the second one will have only 1000 years left to guess. Similarly after two guesses up to 500 years and so on. So, 1000, 500, 250, 125, 63, 31, 15, 7, 3 and then the year will be guessed.

If you liked this problem, go and ask your friends to solve it. And if you liked the game, now you know the trick to win it with ease.

* The puzzle is developed by Dr Gareth Moore.