Mathcounts is best thought of as the maths version of a national spelling bee. Two hundred or so completely awesome young guns are brought together to answer tougher and tougher questions until the top 12 face each other in a speed maths battle to the death.
The 2017 competition was won by Luke Robitaille of Texas, a 13-year-old boy who took less than a second to answer this question.
QUESTION
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?
Now I stress I don't expect you to get it in less than a second, and little Luke has spent thousands of hours practising this sort of stuff, but see if you can find the answer. You might have a good long think about it, but then again you might just pluck it out of midair. … Get it … pluck! Ow.
DO YOU NEED A 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?
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.
Adam Spencer's book The Number Games is available now from all good bookstores or visit www.adamspencer.com.au. Shipping not available to NZ.
