## An elegant puzzle at the New York Times

Joshua Zucker shared this great Numberplay puzzle at the New York Times Wordplay Blog:

Start with a first row with two number ones separated by a space:

Row 1: 1 1

For each subsequent row, insert the sum between each two adjacent numbers, so you get:

Row 2: 1 2 1

Row 3: 1 3 2 3 1

Row 4: 1 4 3 5 2 5 3 4 1

How many 2013s are in row 2013?

## A challenging 11111… puzzle

I received this email from Mr. Brian Silverman who gave me permission to publish it.

I noticed that you were asking for interesting factoids about the number 11.

This isn't quite a factoid about 11 but here's a math puzzle a Russian friend of mine said her son worked out with 7th graders. Seems to me to be beyond most undergrads here. I'm not including the answer, to give you a chance to work on it if you want. but will send it if you ask.

"The question is if it's true that among the numbers consisting of only "1"s (1; 11; 111; 1,111; etc.) there is a number (maybe many) that is divisible by 572,003?

Actually, 572003 is taken arbitrarily. 57 is the number of the school (schools here are mostly numbered instead of having names) and 2003 you possibly know what is recently used for (yes, yes, here in Moscow, too). "

Brian

This puzzle doesn't seem at all obvious to me, especially if one needs to solve it for arbitrary numbers other than 572003. I thought of putting it into my pile of problems to someday solve but then thought it'd be fun to post here.

Can Russian 7th graders solve this? How much help did they get?

Can you solve it?

## A deeper understanding of Rubik’s cube

From MITnews:

## The math of the Rubik’s cube

New research establishes the relationship between the number of squares in a Rubik’s-cube-type puzzle and the maximum number of moves required to solve it.

Erik Demaine, an associate professor of computer science and engineering at MIT; his father, Martin Demaine, a visiting scientist at MIT’s Computer Science and Artificial Intelligence Laboratory; graduate student Sarah Eisenstat; Anna Lubiw, who was Demaine’s PhD thesis adviser at the University of Waterloo; and Tufts graduate student Andrew Winslow showed that the maximum number of moves required to solve a Rubik’s cube with N squares per row is proportional to N^2/log N. “That that’s the answer, and not N^2, is a surprising thing,” Demaine says.

Hat tip to John Cook.

## Review: Monkey Pod Games

Who doesn't like puzzles? I remember playing with devious barrel-shaped wooden puzzles as a kid. I was recently contacted by Rachel at Monkey Pod Games asking if I'd be willing to review one of their puzzles. I always take a look at a company's web-site before I agree to a review as I've discovered that free stuff isn't free since I have to spend time reading a book or playing with a puzzle or game. If I don't like what I see or if I think a product is too expensive to appeal to readers then I won't take a review copy.

I liked what I saw at the Monkey Pod Games site so I humbly agreed to accept a "The Perplexing X in a Box" puzzle. I received it a few days later. It's a devious little puzzle. I couldn't figure it out and I ended up going to the Monkey Pod web-site to get the solution.

## Couple of carnivals and a clever clock conundrum

Two Math carnivals have recently been published:

- The 68th Carnival of Mathematics at +plus magazine
- The 2nd Mathematics and Multimedia Blog Carnival at the Mathematics and Multimedia Blog.

Now, here's a challenging adaptation of a problem I recently discovered. I won't reveal the source till later to not give away the problem.

There's something interesting about the time 2:26 and other times of the day. This interesting thing can be seen over 100 times per day. What is the property and exactly how many times does it occur in a day?

## Mental Floss brain game

Mental Floss is one of my very favorite magazines. Here's a simple (if you see it) puzzle from their web-site:

The answer is here.

## Can you name … ?

## Can You Name All 16 Non-Negative Integers Whose English Names Spell With No Repeating Letters In 10 Minutes?

While there are an infinite amount of numbers, there are, surprisingly, only 16 different non-negative integers (in other words, whole numbers greater than -1) whose names in English, when spelled out, have no repeating letters.

For example, 7 doesn't fit, because when spelled out as S-E-V-E-N, the word has two Es. -2 might seem to work, as it is spelled M-I-N-U-S-T-W-O, and has no repeating letters, but it doesn't qualify because it's negative, and I specified non-negative integers.

Enter as many of these numbers, but you must enter your answers as digits, not spelled out. This keeps spelling from being an issue. If you enter a number greater than 999, you can enter the number with or without commas.

Take the quiz and see how you do.

## Pickover’s picks

Clifford Pickover recently picked ten of his favorite Math puzzles. I found images from Wikipedia to represent them.

How many of the puzzles can you identify from the pictures? (See the bottom of this post for a link to Pickover's article with the answers.)

The puzzles are from here. Hat tip to Shecky at Math-Frolic!

## Terrific Tic Tac Toe Trick

Here's an eerie Tic Tac Toe trick to totally impress your friends. You play a game of Tic Tac Toe with a friend. The game ends in a draw. You pull out a piece of paper (or napkin) that you drew in advance that shows exactly what the ending board would look like. How did you know? Did you control their mind and force them to make the moves you wanted them to?

This great trick is attributed to the late Martin Gardner. It is a great one for kids to learn because it will teach them some things about logical thinking. Hat tip to @grey_matter2 for the trick.

## Pi Day Challenge

[ Editor's Note: Alex Cook is involved in a "Pi Day Challenge" that involves solving 28 puzzles. Alex sent me the following email which I'm forwarding for your enjoyment. Yes, Pi Day was Sunday but the festivities continue! ]

Hello Fellow Math Enthusiasts!

My name is Alex Cook, and I want to let you know about a project I am working on called the Pi Day Challenge.

First off, this project is not exactly my project - it is a project of Matthew Plummer's, a high school teacher from Hanover, MA - I am helping with some of the logistics!

Starting in 2003, Matthew Plummer started creating "Puzzles" on the computer for students. The puzzles were math and logic based. These puzzles were compiled together, put on his school's web site (hanoverschools.org), and then launched on Pi Day (March 14th). The objective was to go through each of the puzzles and make it to the end.