The Answer To This Week's NPR Will Shortz Puzzle Challenge

Mazurland has been quiet for a week now. I'm assuming that the rest of the authors were, as I was, regrouping and preparing themselves for Mazurland's Fifth Anniversary. That's coming up in just four days, and I am sure Mazurland Blog's founder Brother Chris is right now honing a piece to inaugurate our second half-decade. After Chris cracks the bottle over our next 5 years, I'll roll out some posts I've had on the back burner, from chin-rubbers on the big philosophical questions to amusing tales and anecdotes.

Over the years, this Blog has brought you our idiosyncratic observations on a huge variety of topics. Though our pace has slowed a bit recently, we'll continue to give you our peculiar takes on things. And because Mazurland's authors are smart and ahead of the curve, we'll occasionally give you something of value before anyone else, something you can take to the bank.

Today's post is no different. Since none of the Mazur Brothers wrote a New Year's post, I'll knock off that obligation and go one better by giving you the answer to this week's NPR Will Shortz Puzzle Challenge. (OK, I listen to NPR, but only Will Shortz's puzzles and Car Talk!) Here it is:

This challenge comes from Ed Pegg Jr., who runs MathPuzzle.com.

Write down the digits from 2 to 7, in order. Add two mathematical symbols to get an expression equaling 2010. What symbols are these?

Before I tell you the answer, I'll tell you how this came up before the puzzle even aired. It'll show you how the Mazurland synergy works. Last week, Brother Ben posted a comment on Facebook that 2010 is the first year since Lincoln's birth (1809) where the first two digits are double the last two, and that wouldn't happen again until 2211. Now Brother Ben is an über-nerd when it comes to numbers and science (and many other topics). But we Blood Mazurs are not to be outdone. Brother Paul and I have been trading odd observations about years, dates, our ages, and other numerical trivia since Ben was in diapers. So with a bit of thought, I observed that 2010 is the first year that is the product of three consecutive primes (2,3, and 5) and a prime number whose digits are the next two numbers after those three primes (67). A year like this will not occur again until 9345.

Now notice the similarity of my observation to the puzzle. When I heard that puzzle, I immediately grabbed a mental paper and pencil. (I was driving, so I had to work in my head.) The answer I came up with is:

2010 = 2 / 3 X 45 X 67

Notice that there are two mathematical symbols, but one of them is used twice. If you can come up with an answer that only uses two symbols once each, you have my admiration.

[Note: Hats off to reader Tara who found a better solution, using two symbols only once each. See comments for that solution and another challenge.]

Comments

[Tara]

2345 * 6 / 7 = 2010

Fun puzzle!

[Marty]

Damn it! Good answer! That's what fresh eyes will do. I think I just got fixated on the "67" that I thought had to be part of the answer from my related weird observation. Maybe the neat thing about 2010 is the number of ways you can get it out of the first 7 numbers and arithmetic operations. Here's a trivial way to get all the numbers from 0 to 7 and 5 mathematical operations involved:

0 - log(1) + 2345*6/7

There's gotta be a way we can do it with exponentiation, too.

[Hank]

Logarithms? Why not just hand me a nice frothing cup of piss to drink.

Numbers........who needs 'em?

[Marty]

Sorry you don't like logarithms, Hank. Here's one that uses all the numerals from 0 through 9 and only (but all of) the arithmetic operations:

2010 = 0 - (1*2*3) + 4*567*8/9

[Marty]

Duh. This one gets all four arithmetic operations (some more than once), exponentiation and logarithms, and all nine numerals, in order. Parentheses were needed:

2010 = exp(0)*(log(1) - 2*3 + 4*567*8/9)

[Hank]

Marty-You are aware that I was offically diagnosed with pathological Math Block at a young age. Just doesn't make any sense to me. The only math that I have used in my adult life I learned between 1st and 9th grade. And that included Pharmacy Math.

Fractions, decimal equivalents (for Machine Shop work) and Algebra. Haven't had the need for Geometry since 1972 when I got a mercy 65 on the Regents. Took "Dummy Math 11", and didn't learn much more there either.

Now I know there must be a use for all the high mathematics that you teach at Penn State, but I doubt strongly the average Joe needs a bit of it.

[Marty]

Hank, you've mentioned your math block before. But the original puzzle requires no higher math. Heck, if it's given on NPR, and if Tara, who's a Librarian educated at a liberal arts school, can trump the answer of Mr. High-Falootin' Math, it can't be for math-Einsteins only.

[Tara]

I did take a calculus course at that liberal arts school! While I'm no math nerd, my trick for getting through track workouts has always been to do math problems in my head. I realize to some people that's like saying my trick for alleviating the pain from hitting myself with a hammer is to get a second hammer.

[Marty]

I'm always doing math problems in my head, except when I'm running. Oxygen level too low. I've always told you, Tara, that you should be running faster...

When I run on the track at Rec Hall, I have enough trouble counting laps. I think I'd have trouble figuring out if a two-digit number is prime.