Can you solve this tricky maths riddle in one second?
A 13-year-old genius solved this tricky maths riddle in just one second. How long will it take you?
The headscratcher comes from the Mathcounts National Mathematics competition in the United States, which is like a maths version of a national spelling bee.
The 2017 competition was won by 13-year-old Luke Robitaille of Texas, who took less than a second to answer this riddle.
Riddle: In a barn, 100 chicks sit peacefully in a circle. Suddenly, each chick randomly pecks the chick immediately to its left or its right. Each chick pecks only once, and is not affected by which way its neighbours peck. What is the most likely number of unpecked chicks?
Mathematical genius Adam Spencer, whose new book The Number Games is out now, offers this hint.
“Imagine you are one of the chickens in the circle. What are all the possible ‘peckings’ that could happen to you, including not getting pecked, and what are the odds of each of those ‘peckings’ happening? Run these odds out over the 100 chickens and what number of ‘no pecks’ do you get?” he tells news.com.au.
Still haven’t got it yet? Here’s the answer, as explained by Spencer.
Answer: For every chicken, the odds of getting pecked from the right is 0.5 and the odds of not getting pecked from the right is 0.5. Obviously the odds are the same for getting pecked from the left. So the odds of getting ‘double pecked’ are 0.5 x 0.5 = 0.25. The odds of getting ‘not pecked’ are also 0.5 x 0.5 = 0.25. The odds of getting ‘single pecked’ are 0.5 (0.25 from the left plus 0.25 from the right). Across 100 chickens you’d expect 25 to remain unpecked — you’d also expect 25 to be double pecked and 50 to be pecked once only.