Pickles AcademyStart for freeBinary search – practice for Years 7–9
Sample questions on Binary search with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.
- Subject
- Computing
- Year
- Years 7–9
- Curriculum area
- Information systems
Question types: Guessing a number by halving
Rule: Binary search
Always guess the middle of the numbers that are left. Each answer rules out about half.
n guesses are enough when 2ⁿ − 1 is at least how many numbers there are: 7 numbers 3 guesses, 15 numbers 4, 1000 numbers 10.
Example: 1 to 100: 2⁷ − 1 = 127 is enough, 2⁶ − 1 = 63 is not → at most 7 guesses
Watch out: Don’t guess one by one from the start: with 100 numbers it could take almost 100 guesses.
Sample questions
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Question 1 Easy
I am thinking of a whole number from 1 to 31. To each guess I answer “higher”, “lower” or “correct”. How many guesses do you need at most if you always guess the middle of the numbers that are left?
Show the solution
Answer: 5How it works: Each guess at least halves what is left: 2^4 = 16 ≤ 31 < 2^5 = 32, so 5 guesses.
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Question 2 Normal
I am thinking of a whole number from 1 to 530. To each guess I answer “higher”, “lower” or “correct”. How many guesses do you need at most if you always guess the middle of the numbers that are left?
Show the solution
Answer: 10How it works: Each guess at least halves what is left: 2^9 = 512 ≤ 530 < 2^10 = 1024, so 10 guesses.
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Question 3 Hard
I am thinking of a whole number from 1 to 80. To each guess I answer “higher”, “lower” or “correct”. You always guess the middle of the numbers that are left (the smaller of the two middle ones when their count is even). With which guess do you hit 54?
Show the solution
Answer: 7How it works: Guesses: 40, 60, 50, 55, 52, 53, 54.
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