Wolfram Research, the folks behind Mathematica, have just started posting puzzles to go with the episodes of the hit show, NUMB3RS.
From the Wolfram Blog:
Wolfram Research has worked with the CBS/Paramount show NUMB3RS since its first season. Now in the fifth season, it remains the most popular show of Friday nights. “The Math behind NUMB3RS” gives a more in-depth look at some of the mathematics in each episode. With season 5, we’ve added a math puzzle to go with each episode. Fifteen episodes into season 5, there are fifteen puzzles available.
For each puzzle we make a web page with an episode file that contains the puzzle itself, a hint section that discusses the related mathematics, a quote from the episode, and a detailed solution. For example, in episode 509, “Conspiracy Theory,” the puzzle is “Nonrandom Matrix“—a type of Latin square also known as a Sudoku puzzle. In a Sudoku puzzle, you must fill in the matrix so that every row, column, and 3×3 box contains the digits 1 through 9.
Blinkdagger has MMM #26 posted. This one is tricky. We've received a number of different answers and even the incorrect ones are well explained!
So, if you want a Blinkdagger-style Math problem, give this one a try!
Here's the problem description:
Ever since Quan was a little boy, his lifelong dream has been to fly around the world in an airplane.
- Quan lives on an island wherein there are 100 airplanes, all created equally with identical characteristics.
- Each airplane has a fuel tank that contains enough fuel to fly exactly half way around the world.
- All of the airplanes travel at the same speed, and use their gas at the same rate.
- Airplanes can exchange fuel with other airplanes while in flight.
- The island is the only source of fuel.
- For the purposes of this problem, assume that there is no time lost refueling on either the air or ground.
- All airplanes must make it back to the island safely.
Question: What is the lowest number of airplanes required to allow one airplane to travel all the way around the world?
Check out the rules and submission information at Blinkdagger.
Ron Frederick is the winner of MMM #25: Monotonous Monday Math Madness. Congratulations, Ron!
Jonathan had a very simple explanation, based on elementary combinatorics:
Line up the digits 123456789 and take any one of them: C(9,1) choice.
Take any two of them: C(9,2).
Now, wait. Am I saying there are C(9,2) = 36 2-digit ascending numbers? 12, 13, 14, 15, 16,17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89. Yup, thirty-six of them.
So we have [ C(9,1) + C(9,2) + C(9,3) + C(9,4) + C(9,5) + C(9,6) ] / 1,000,000 = [9 + 36 + 84 + 126 + 126 + 84]/1,000,000 = .000465
Blinkdagger has the next MMM so check their site on Monday.