Here’s a nice brain teaser for you. Remember this gem that Tootsie Pops aired beginning in 1969?
Well, let’s see if we can apply the same question to Brain Chase treasure hunts (but have a slightly more disciplined approach than the owl):
Q: If a Brain Chase treasure is buried somewhere on earth and we need to guess within a two-mile radius to win, how many clicks would it take to find it?
A: Let’s turn this into an equation, and solve it.
We know we could always get lucky and find it on the first guess, but let’s solve for the MAXIMUM number of guesses it would take to find the globe. We’d just need to find the total surface area we’re searching in, then divide that by the surface area of each guess, like this:
Total “eligible” surface area / area of each guess = maximum # of guesses required
Next, let’s define what we mean by “eligible” surface area. We’ll need to make some assumptions here, but let’s keep it simple. We know the globe is hidden somewhere on land – and not underwater – because it’s buried beneath a rose bush. According to info.com, approximately 70% of the earth’s surface is covered with water, leaving only 30% land. That’s about 59,100,000 square miles. We could divide this further by making other assumptions about climate, proximity to cities, etc., but for now let’s just assume it’s buried anywhere on solid ground. So our numerator is around 59,000,000 square miles.
Then we need to figure out the approximate area of each guess. We know that the first to guess within a two-mile radius of the treasure will win – so let’s be sure not to waste guesses by selecting two points within the same two-mile radius. But how much surface area is that? The equation for the area of a circle is pi* r^2 (click here to see how Khan Academy teaches about finding the area of circles). We already know the radius (2), and we know that 2 squared is 4. So multiplying 4 by pi will give us the area of each guess. Our guess area is 12.57.
Finally, we need to solve the equation by dividing total land area of 59,000,000 square miles by each guess of 12.57 square miles:
59,000,000 / 12.57 = 4,693,715
At one guess per day, that’s 4.7 million days, or about 12,900 years! Keep in mind, Brain Chase is a six-week challenge, so at most, you’ll get one guess per day, or 42 total guesses (unless no one is able to locate the treasure, in which case more clues will be delivered and the guessing will continue until the treasure is found!). With only 42 guesses, you’ll have to make each guess count.
But don’t worry – if you’re keeping up with the Learning Challenge and unlocking the clues, you just might find a trail of bread crumbs that leads you right to the prize. Stay on your toes!
Think you know a better way to calculate the number of clicks it will take? See any problems with this methodology? Share your thoughts with us! We’d love to hear!
(PS – a chemical engineering doctorate student from the University of Michigan reported that it takes 411 licks to get to the center. That’s worth a Nobel Prize or something, isn’t it?)