## Archive for January, 2017

### 2 Good 2 Be True

I was eating a bowl of shepherd’s pie at the Irish pub in our neighborhood. A man walks up to my table and asks, “What’s your favorite number?”

“Uh, 153,” I respond.

“And 153 × 2 is 306,” he says, then hurriedly scurries away.

He approaches another table, asks another patron for her favorite number, and again multiplies it by 2. He does this over and over, popping from table to table, annoying customer after customer. Eventually, the manager notices this eccentric behavior and approaches the man.

“Sir,” says the manager, “You can’t keep interrupting people’s dinners by asking them for a number and then multiplying by 2.”

“What can I say,” he responds. “I love Dublin!”

A little while later, the gentleman at the table next to me says to his companion, “I know a sure-fire way to double your money.”

This piqued my interest, so I leaned over to eavesdrop on his advice.

“Fold it in half,” he said.

Dismayed that you’ve read this far and have only heard two terrible jokes? Well, buck up, because your fortune is about to change. I can’t help you double your money, but I can help you get twice as much for it.

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### 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 2017
^{2017}has 6,666 digits. - 2017 = 44
^{2}+ 9^{2} - 2017 = 12
^{3}+ 6^{3}+ 4^{3}+ 2^{3}+ 1^{3}= 10^{3}+ 9^{3}+ 6^{3}+ 4^{3}+ 2^{3}

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.