Math Problem for 2017
Happy New Year! Welcome to 2017.
Here are some interesting facts about the number 2017:
- It’s prime. (Okay, so that fact isn’t very interesting. But just you wait…)
- Insert a 7 between any two digits of 2017, and the result is still a prime number. That is, 27,017, 20,717, and 20,177 are all prime. (See? Told you it was gonna get better.)
- The cube root of 2017 is approximately 12.63480759, which uses all ten digits 0‑9, and 2017 is the least positive integer that has this property. (Mind blown yet?)
- The decimal expansion of 20172017 has 6,666 digits.
- 2017 = 442 + 92
- 2017 = 123 + 63 + 43 + 23 + 13 = 103 + 93 + 63 + 43 + 23
If you need some more, check out Matt Parker’s video.
Sorry, no video from me. But in honor of our newly minted prime year, I have created a problem for you to solve.
In the area model below (not to scale), the area of the five blue regions is indicated by the number inside the rectangle. What is the area of the yellow region with the question mark inside?
Sorry, I don’t give answers. Feel free to have at it in the comments.