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Whether or not you're staying at home binging Stranger Things 2 or out Trick or Treating with the little Batman fans in your life, there's plenty of Batman comics to enjoy this holiday season! Listen in as Londyn candidly discusses some of her favorite reads from different eras of the Dark Knight! Eric Anderson and Marty Ambrose will be the guests on the show today. Anderson's thrilling "New Caliphate" trilogy, picks up where OSIRIS left off, on a roller-coaster of soldiers, spies, statesmen and sellouts, all thrown together either to save the world—or see it destroyed.

With an outrageously enigmatic US president dead, his most hated political opponent about to be inaugurated, and ISIS attacking on multiple global fronts, will America and her allies give in to the jihadi and withdraw from the Middle East? The only way for More and Faheem to prevent the crisis from becoming a catastrophe is to turn to More's nemesis ODIN—the ultimate cyber-warrior. With rivers of blood ready to run through the capitals of Europe, Africa, and Washington, D. The biggest podcast Legends Library has ever done is here! Dianna started out life as a photorealistic artist and launched her first business at the age of seventeen out of necessity.

She was living on her own and working two jobs so she started painting signs and murals every free minute she could find. Years later, while painting over a hundred feet in the air, she started making up stories to keep herself entertained during the long days. This is a copyrighted, trademarked podcast owned solely by the Authors on the Air Global Radio. New York Times Freakonomics News. Takeru Kobayashi revolutionized the sport of competitive eating. What can the rest of us learn from his breakthrough? Mary will discuss her new radio show, the HoneyB Morrison Show and three of her latest books.

Morrison believes that women should shape their own destiny. Born in Aurora, IL, and raised in New Orleans, LA, she took a chance and quit her near six-figure government job to self-publish her first book, Soulmates Dissipate, in and begin her literary career. Mary is actively involved in a variety of philanthropic endeavors, and in she sponsored the publication of an anthology written by 33 sixth-graders.

Then it features three triangles: It also provides someone's answers to this naming test: We agreed that Trump is scarier. At this time he seemed his usual self. I offered John a ride home, as I do whenever I visit him. He was very glad as he felt very tired. He started to get up. This time, I remembered not to try to help. He couldn't get up, I waited. He tried to push his weight off the table top, but the table was wobbly. I leaned on the table, as if to rest. We often play this sort of game in which he welcomes my help as long as we both pretend that I'm not helping.

My car was a block away and he wanted to walk the block. But after making two steps out of the pizzeria he changed his mind and asked me to bring the car to him. This was the first time ever. This visit he was so much worse than ever before. I dropped him off at his house and offered to walk him to the door. I sat in my car and watched him walking very slowly along his path. I had this sinking feeling in my gut that I was seeing John for the last time.

I drove away, once he disappeared behind his door. In Edison, my car started beeping and I panicked. I was far away from home, and didn't want to be stuck in NJ. I started to look for the source of the sound. It was John's phone. As always, my gut feeling deceived me: I had to go back to Princeton. I drove back to John's apartment.

His door was unlocked and I entered. He was resting in bed. He was greatly annoyed at being disturbed. I explained the reason, and gave him his phone. He took the phone and said, "Off you go. The submitted file is here: This is a math blog, but from time to time, I write about other things.

Today I have something to say about puns, which I adore. I also like gym, but rarely go there: I stopped using stairs, because they are up to something. I wanted to learn how to juggle, but I don't have the balls to do it. I work at MIT, the work place with the best dam mascot: My salary is not big, and I stopped saving money after I lost interest.

I'm no photographer, but I have pictured myself outside of MIT too. I am a mathematician, which is the most spiritual profession: I am very comfortable with higher powers. I praise myself on great ability to think outside the box: I am also a bit of a philosopher: I can go on talking about infinity forever. I would love to tell you a joke. I recently heard a good one about amnesia, but I forgot how it goes.

My biggest problem is with English. So what if I don't know what apocalypse means? It's not the end of the world! Sign-up for a premium-rate telephone number through which you make money from every call. Take a loan at the bank. Do not pay back. Collection agencies start calling non-stop.

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A cafe patron ordered a pastry, then changed his mind and replaced it with a cup of coffee. When he finished his coffee, he started leaving without paying. The waiter approached him: At a farmers market stand there is a sign: A client requests one melon and pays 3 dollars, then repeats the procedure two more times. This is really stupid. This happens all the time: If the government listens in on my phone conversations, should they be paying half of my phone bill? If your poker opponent got lucky cards four times in a row, he must get lousy cards now.

Nope, the deals are independent; prior observations have no bearing on the next deal. The opponent is cheating; get away from the table now! I recently posted two geometry problems. Now is the time for solutions:. Is it possible to put positive numbers at the vertices of a triangle so that the sum of two numbers at the ends of each side is equal to the length of the side?

One might guess that the following numbers work: But there exists a geometric solution: The tangent points divide each side into two segment, so that the lengths of the segments ending at the same vertex are the same. Assigning this length to the vertex solves the problem. Surprisingly, or not surprisingly, this solution gives the same answer as above. Prove that it is possible to assign a number to every edge of a tetrahedron so that the sum of the three numbers on the edges of every face is equal to the area of the face. The problem is under-constrained: There should be many solutions.

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But the solution for the first problem suggests a similar idea for the second problem: Construct the inscribed sphere. Connect a tangent point on each face to the three vertices on the same face. This way each face is divided into three triangles. Moreover, the lengths of the segments connecting the tangent points to a vertex are the same. Therefore, two triangles sharing the same edge are congruent and thus have the same area. Assigning this area to each edge solves the problem. There are many solutions to the second problem. I wonder if for each solution we can find a point on each face, so that the segments connecting these points to vertices divide the faces into three triangles in such a way that triangles sharing an edge are congruent.

What would be a geometric meaning of these four points? I am pleased that the hunt got very positive reviews from the participants. I spent tons of hours working on the hunt and it is good that folks liked it. I edited and tested a lot of puzzles. Here is my review of these year's puzzles that are math-related. I already posted an essay about the puzzles I wrote myself. Four of my five puzzles are math-related, so I am including them below for completeness. I will mention the topic of each puzzle unless it is a spoiler. I start with Nikoli-type puzzles. Four elegant Nikoli-type puzzles were written or cowritten by Denis Auroux.

In all of them the rules of the logic are stated at the beginning. That means the logic part doesn't contain a mystery and can be solved directly. Five pirates discovered a treasure of gold coins. They decide to split the coins using the following scheme. The most senior pirate proposes how to share the coins, and all the pirates vote for or against it.

Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the next most senior pirate making a proposal. As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins whether he votes for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard.

Assuming that all five pirates are intelligent, rational, greedy, and do not wish to die, how will the coins be distributed? You can find the solution in many places including Wikipedia's Pirate game. The answer is surprising: I always hated this puzzle, but never bothered to think through and figure out why. This puzzle emphasizes the flaws of majority voting. The procedure is purely democratic, but it results in extreme inequality. That means a democracy needs to have a mechanism to prohibit the president from blatantly benefiting himself.

With our current president these mechanisms stopped working. Given that Trump does everything to enrich himself, the pirates puzzle tells us what to expect in the near future. We, Americans, will lose everything: I was on the writing team of this year's hunt, which was based on the movie "Inside Out.

Our first round consisted of 34 puzzles related to five basic emotions: Each emotion had its own meta puzzle. And the round had a meta-meta puzzle and a runaround. As I tend to write easy puzzles, I contributed three puzzles to this emotions round. The puzzles had references to corresponding emotions that were not needed for the solve path. They were inserted there for flavor. I also wrote another easy puzzle called A Tribute: Though the puzzle is easy, it is useful in solving it to be familiar with the MIT mystery hunt.

This is why the puzzle didn't fit the first emotions round. I also wrote a very difficult puzzle called Murder at the Asylum. This is a monstrosity about liars and truth-tellers. The solution goes like this. Consider divisibility of this number by 9. The sum of the digits is That means the number is divisible by 3, but not by 9. Therefore, it can't be a square. Why do we consider divisibility by 9?

The divisibility by 9 is a very powerful tool, but why was it the first thing that came to my mind? The divisibility by 9 doesn't depend on the order of the digits. Whenever I see a problem where the question talks about digits that can be in any order, the first tool to use is the divisibility by 9. The why question, is very important in mathematics. But it is also very important in life. It took me many years to start asking why people did this or that.

I remember my mom was visiting me in the US. Every time I came back from work, she complained that she was tired. Because she did the laundry in the bath tub. She wouldn't use my washing machine, because she didn't have such a thing in Russia. I promised her that I'd do the laundry myself when there was a sufficient pile. However, she insisted that the dirty clothes annoyed her.

I would point that my water bill went up. We argued like this every day. We were both frustrated. Then I asked myself why. Why does she do the laundry? The answer was there. She wanted to be helpful. I calmed down and stopped arguing with her. I sucked it up and paid the water bills.

Her time with me turned into the most harmonious visit we ever had. Unfortunately, it was the last. I kept forgetting my password, so I changed it to "incorrect". Now, when I make a mistake during login, my computer reminds me: Quantum entanglement is simple: Still the larger half of my class doesn't get it. This puzzle is tricky only because of gender-bias. Most people assume that the professor is male and miss the obvious intended solution, in which a female professor is watching her brother fighting with her husband.

Years ago people couldn't figure out this puzzle at all. So there has been progress. I was glad that my students suggested so many ideas that work. Nonetheless, many of them revealed their gender-bias by initially assuming that the professor is a man. Correction Nov 11, Replaced "the same distance from" with "halfway between" to eliminate the possibility of the plumber living in the yellow house. Thank you to my readers for catching this mistake and to Smylers for suggesting a correction. The solution to the second problem is to color the shape as a chess board and check that the number of black and white squares is not the same.

What is interesting about the first problem is that it passes the color test. It made me wonder: Is there a way to characterize the shapes on a square grid that pass the color test, but still can't be covered in dominoes? How to restore justice: Create a folder named Justice. Go to the trash bin and click restore. When you sign up, you are friends with everyone. Then you send un-friend requests. The first puzzle is now called the Fractal Word Search. It is available on the Hunt website under its name In the Details. I posted one essay about the puzzle and another one describing its solution.

Unfortunately, the puzzle is not available, but my description of it is. Today let's look at the third puzzle Derek made for the Hunt, building on an idea from Tom Yue. This is a non-mathematical crossword puzzle.

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Derek tends to write multi-layered puzzles: You think you've got the answer, but the answer you've got is actually a hint for the next step. Often multi-layered puzzles get solvers frustrated, but the previous paragraph is a hint in itself. If you expect the difficulty, you might appreciate the fantastic beauty of this puzzle.

Welcome to Ex Post Facto. Every time I visit Princeton, or otherwise am in the same city as my friend John Conway, I invite him for lunch or dinner. I have this rule for myself: I invite, I pay. If we are in the same place for several meals we alternate paying. Once John Conway complained that our tradition is not fair to me. From time to time we have an odd number of meals per visit and I end up paying more. I do not trust my memory, so I prefer simplicity.

I resisted any change to our tradition. We broke the tradition only once, but that is a story for another day. Let's discuss the mathematical way of paying for meals. Many people suggest using the Thue-Morse sequence instead of the alternating sequence of taking turns. If this is the order of paying for things, the sequence gives advantage to the second person.

So the suggestion is to take turns taking turns: If you are a nerd like me, you wouldn't stop here. This new rule can also give a potential advantage to one person, so we should take turns taking turns taking turns. Continuing this to infinity we get the Thue-Morse sequence: Some even call this sequence a fair-share sequence.

Should I go ahead and implement this sequence each time I cross paths with John Conway? Actually, the fairness of this sequence is overrated. I probably have 2 or 3 meals with John per trip. If I pay first every time, this sequence will give me an advantage. It only makes sense to use it if there is a very long stretch of meals. This could happen, for example, if we end up living in the same city. But in this case, the alternating sequence is not so bad either, and is much simpler. Many people suggest another use for this sequence.

Suppose you are divorcing and dividing a huge pile of your possessions. A wrong way to do it is to take turns. First Alice choses a piece she wants, then Bob, then Alice, and so on. Alice has the advantage as the first person to choose. An alternative suggestion I hear in different places, for example from standupmaths , is to use the Thue-Morse sequence. I don't like this suggestion either. If Alice and Bob value their stuff differently, there is a better algorithm, called the Knaster inheritance procedure , that allows each of them to think they are getting more than a half.

If both of them have the same value for each piece, then the Thue-Morse sequence might not be good either. Suppose one of the pieces they are dividing is worth more than everything else put together. The beauty of the Thue-Morse sequence is that it works very well if there are a lot of items and their consecutive prices form a power function of a small degree k , such as a square or a cube function.

You might think that if the sequence of prices doesn't grow very fast, then using the Thue-Morse sequence is okay. Here is the sequence of prices that I specifically constructed for this purpose: Alice gets an extra 1 every time she is in the odd position. This is exactly half of her turns. That is every four turns, she gets an extra 1.

If the prices grow faster than a power, then the sequence doesn't work either. Suppose your pieces have values that form a Fibonacci sequence. Take a look at what happens after seven turns. We see that Alice gets more by F n This value is bigger than the value of all the leftovers together. I suggest a different way to divide the Fibonacci-priced possessions. If Alice takes the first piece, then Bob should take two next pieces to tie with Alice. I can combine this idea with flipping turns. After that we can continue and flip the whole thing: Then we flip the whole thing again.

And again and again. At the end we get a sequence that I decided to call the Fibonacci fair-share sequence. Now it's solution time. First we show that we can do this in 70 weighings. The strategy is to compare one coin against one coin.

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If the scale balances, we are lucky and can stop, because that means we have found two real coins. If the scale is unbalanced, the heavier coin is definitely fake and we can remove it from consideration. In the worst case, we will do 70 unbalanced weighings that allow us to remove all the fake coins, and we will find all the real coins.

The more difficult part is to show that 69 weighings do not guarantee finding the real coin. We do it by contradiction. Suppose the weights are such that the real coin weighs 1 gram and the i -th fake coin weighs i grams. That means whatever coins we put on the scale, the heaviest pan is the pan that has the fake coin with the largest index among the fake coins on the scale. Suppose there is a strategy to find a real coin in 69 weighings.

Given this strategy, we produce an example designed for this strategy, so that the weighings are consistent, but the collector cannot find a real coin. For the first weighing we assign the heaviest weight, 70 to one of the coins on the scale and claim that the pan with this coin is heavier. If a weighing has the coins with assigned weights, we pick the heaviest coin on the pans and claim that the corresponding pan is heavier.

If there are no coins with assigned weights on pans, we pick any coin on the pans, assigned the largest available weight to it and claim that the corresponding pan is heavier. After 69 weighings, not more than 69 coins have assigned weights, while all the weighings are consistent.

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The rest of the coins can have any of the leftover weights. For example, any of the rest of the coins can weigh grams. That means that there is no coin that is guaranteed to be real. I stumbled upon a couple of problems that I like while scanning the Russian website of Math Festival in Moscow The problems are for 7 graders. This problem is really very difficult. The competition organizers offered an extra point for every diagonal on top of The official solution has 24 diagonals, but no proof that it's the longest. I'm not sure anyone knows if it is the longest.

The year is The man on the left is my first husband, Alexander Goncharov. Although we were out of touch for a decade, when I married my third husband, Joseph Bernstein on the right , Goncharov started visiting us. It wasn't me he was interested in: I found this situation hilarious, so I took this photo. But that's not all. My second husband, Andrey Radul, is not in the picture. But all four of us were students of Israel Gelfand.

In short, my three ex-husbands and I are mathematical siblings — that is, we are all one big happy mathematical family. The Best Writing on Mathematics is out. At the end of the book there is a short list of notable writings that were considered but didn't make it. The "short" list is actually a dozen pages long. And it includes two more papers of mine: Mathematical Research in High School: To continue bragging, I want to mention that my paper A Line of Sages was on the short list for volume.

And my paper Conway's Wizards was included in the volume. I like Odd-One-Out puzzles that are ambiguous. Look at the cover: The book doesn't include answers, but it has nine more examples in each of which there are several possible odd-one-outs. I married an American citizen and moved to the US in At the time I was a very patriotic Russian. It took me a year of pain to realize that some of my ideas had been influenced by Soviet propaganda. After I washed away the brainwashing, I fell in love with the US. For 25 years I thought that America was great.

For the last several months I've been worried as never before in my life. I feel paralyzed and sick. To help myself I decided to put my feelings in words. My mom was 15 when World War II started. The war affected her entire life, as well as the lives of everyone in the USSR.

Every now and then my mom would tell me, "You are lucky that you are already 20 and you haven't witnessed a world war. From time to time I tell myself something like, "I am lucky that halfway through my expected lifetime, I haven't had to live through a world war. To maintain the peace is a difficult job. Everything needs to be in balance. Trump is disrupting this balance. I am worried sick that my children or grandchildren will have to witness a major war. I've noticed that, as a true showman, Trump likes misdirecting attention from things that worry him to fantastic plot twists that he invents.

What's the best way to make people forget about his tax returns? It's the nuclear button. Dropping a nuclear bomb some place will divert people from thinking about his tax returns. As his plot twists are escalating, is he crazy enough to push the button? The year was the warmest on record. The year was even warmer.

And last year, , was even warmer than that. I remember Vladimir Arnold's class on differential equations. He talked about a painting that had been hanging on a wall for 20 years. Then it unexpectedly fell off. Mathematics can explain how such catastrophic events can happen. I keep thinking about our Earth: My grandchildren might not be able to enjoy beaches and forests the way I did. What if, like the fallen painting, the Earth can spiral out of control and completely deteriorate?

But Trump is ignoring the climate issues. Does he care about our grandchildren? I am horrified that Trump's policies will push climate catastrophe beyond the point of no return. Wiretapping is not wiretapping. Phony jobs numbers stopped being phony as soon as Trump decided that he deserved the credit. The news is fake when Trump doesn't like it. Trump is a pathological liar; he assaults the truth. Being a scientist I am in search of truth, and Trump diminishes it. I do not understand why people ignore his lies. Two plus two is four whether you are a democrat, or a republican, or whomever.

Facts are facts, alternative facts are lies. I am scared that lies have become acceptable and no one cares about the truth any more. I lived in Russia for the first unhappy half of my life, and in the US for the second happy half. I do not want to go back. There is something fishy between Putin and Trump. Whether it is blackmail or money, or both, I do not know the details yet, But Trump is under Putin's influence. Trump didn't win the elections: I do not want to go back to being under Russian rule. I grew up in a country where the idea of a good husband was a man who wasn't a drunkard.

Encouragement from my fellow writers became the primary motivation for writing the book. What kind of research did you do to write your book? That means I read a lot of court cases involving writers. I also read the federal laws on copyright and trademark.

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I love the theme that runs through your book, which is based on Alice in Wonderland and other works by Lewis Carroll. Did you face any challenges when writing this book? Finding the right Lewis Carroll quotes was challenging but also fun. The hardest task was choosing which cases to use. If I had tried to read everything, I would still be reading. So I narrowed it down to three categories: Of course, I also picked cases that make an important legal point.

What encouragement has helped you along your way? Good critique partners were my best encouragement. My husband was supportive, too. You are a licensed attorney. How does that experience inform, inspire, and affect your writing? On the blessings side, my legal training and experience have taught me to love research and to do it well.

It also gives me something to write about: On the curse side, I have spent years trying to learn how NOT to write like a lawyer. Your current book is NF for adults, but you also write for children. Can you tell us a little about your writing life?