How the heck? A puzzle with a very surprising answer

A few weeks ago I posted a puzzle about two mathematicians guessing the results of coin tosses. Dwight asked me about generalizations to more than two mathematicians. While the problem may seem very different on the surface, in my opinion the underlying issue is actually quite similar and the changes are necessary to generalize from two mathematicians to N.

I posted one version a while ago here which I will repeat as a warmup for the harder version 🙂

16 mathematicians are in a room. They are each assigned a hat, either black or white. Each hat is assigned totally independently of all the other hats and has a 50% chance of being either color. Each mathematician can see everyone else’s hat but not his/her own hat. The mathematicians all have to independently and simultaneously guess the color of their own hat. They have an hour before the hats are assigned to make a plan, then one minute to view the hats, then they each go into a voting booth to vote for the color of their own hat. While they are viewing the hats they can not communicate or signal in any manner to the other mathematicians.

The success or failure of the mathematicians is judged as a team: if every single one guesses their own hat color correctly, the team wins. If even a single mathematician guesses incorrectly, the team loses. What are the odds of their success, and what strategy should they employ to achieve it? [Hint: the odds are much better than you might first think they are. Really. If you are sure you can’t improve them I am happy to find a jurisdiction where we can play this for high stakes!]

Second version (if you thought the first version was too easy):

Everything is just like the first version, except that when the mathematicians enter the voting booth they can vote “White”, “Black”, or “Don’t know”. If anyone is wrong, they all lose. If everyone passes, they all lose. If at least one mathematician chooses a color and all mathematicians who choose colors are correct, they win. Again, what are the odds of their success, and what strategy should they employ to achieve it? Again, you can do better than you might first think!

— Max

Math puzzle with a surprising answer

16 mathematicians are imprisoned by the evil emperor. They are told that in the morning they will each be assigned a hat, either white or black. Each hat is assigned randomly (50/50) and independently. Each mathematician will be able to see everyone else’s hat but not their own. After one minute to observe the hats, they will simultaneously be sent back to their private cells where they have to guess the color of their own hat. If a single mathematician guesses incorrectly, they will all be executed. If all 16 guess correctly, they go free.

What is the probability that the mathematicians will be set free, and how should they guess?

If you’d like a hint, look at this problem. Thanks to Dwight for suggesting more complex problems in that spirit; if this isn’t hard enough I’ll add another twist next week.

— Max

Fun math puzzle: two mathematicians and a coin…

The king is very angry at his two best mathematicians, but rather than executing them immediately institutes the following process:

They are banished to opposite ends of the kingdom, kept under 24 hour guard. Every day  in both Westerville and Eastgate where the mathematicians are being kept one of the guards flips a coin and records the result. Each mathematician must then guess the result of the flip at the other end of the kingdom. A messenger is then dispatched from each location to the royal palace to share the results of the flip and their mathematician’s guess. As long as one of the two mathematicians guesses right, the lives of both mathematicians are spared until the next day. The first day that both mathematicians are wrong, they are both executed.

The king imagined this game would not last more than a week or so. The mathematicians, however, hatched a clever plan as they were being ushered out the door of the castle.

What do the mathematicians do to live as long a life as they can, and on average how long should the king have to wait to execute them?

— Max

How much would you pay to own an undisclosed percentage of my house?

I just got an email from a friend describing the interview offer process of a mutual friend joining a technology startup. The newly minted employee has an offer but they won’t tell him how many shares are outstanding. He was told what percentage of the “employee pool” he was getting, but not the overall percentage. What exactly is included in the “employee pool” is a question – is it just unissued options, is it akk issued and unissued options, is it all common shares including founders???

As I’ve said before when talking about stock options (see this post), it is impossible to evaluate your grant without knowing how many total shares are outstanding. Proof by analogy: how much would you pay for partial ownership of my house? I can create an “investor pool” which represents some ownership of my house. For $50,000, you can own 10% of the investor pool. Sorry, but I am unable to disclose how much of the ownership of my house will be assigned to the investor pool. Please contact me if you are interested! I don’t expect to sell much of my house this way; why should I expect employees to be excited about options offered in the same manner?

Not only does the lack of data make it hard to evaluate the stock grant, but the lack of transparency is concerning as well. One of the things that makes startups great is a team working together towards a common goal. For me, a big part of creating that is giving the team a lot of transparency about the company they are building. I view the employees in an early stage company as stakeholders, and as investors in a sense: they are investing their time, their passion, and their reputation in the company. To not share basic information, especially at an early stage, demeans that investment and undermines the sense of team.

Will my friend still join? Maybe. There’s a lot to like about the opportunity. But the lack of data and the lack of transparency is a red flag. At a minimum, it’s caused an extra round of digging/assessment. As an employer, why would you want to give a potential recruit a reason to question your offer?

— Max

HP/Autonomy and Oracle/Endeca: Is everything now “big data”?

The industry has a tendency to attach everything to the latest hot trend/buzzword, but I just can’t accept Autonomy and Endeca as “big data” vendors.

Autonomy is a search engine vendor that added various content technologies like Zantaz (email archiving) and Interwoven (web content management). Yes, it has “unstructured” in common with big data, but that’s about it.

Endeca started as an ecommerce search engine with aspirations of general-purpose BI tool. So it has “analytics” in it but again, I don’t see it as big data.

I’m not saying that either Autonomy or Endeca is a bad technology, if they are big data then maybe Sharepoint is big data too.

Does anyone out there really think these enterprise search-in-disguise vendors are big data?

— Max

Richard Stallman offensive remarks on Steve Jobs death

I love free software, and Richard Stallman has done much to advance it, but this time he’s really gone too far.

From his blog:

“Steve Jobs, the pioneer of the computer as a jail made cool, designed to sever fools from their freedom, has died.

As Chicago Mayor Harold Washington said of the corrupt former Mayor Daley, “I’m not glad he’s dead, but I’m glad he’s gone.” Nobody deserves to have to die – not Jobs, not Mr. Bill, not even people guilty of bigger evils than theirs. But we all deserve the end of Jobs’ malign influence on people’s computing.

Unfortunately, that influence continues despite his absence. We can only hope his successors, as they attempt to carry on his legacy, will be less effective.”

I can’t speak on behalf of the entire open source community, but I can say that Richard Stallman certainly does not on this point.

My quick take:

Apple, under Jobs leadership, built some great products. They weren’t free (like beer or speech), but they moved the industry forward. Would it have been even better if they were free? Sure. But that’s a different world. I’m glad that folks have the freedom to make great software which is free and great software which is not. “Freedom” can be its own tyranny.

Love to hear your thoughts…

— Max

A math puzzle that’s harder than it sounds

A room is 30 feet long, 12 feet wide, and 12 feet high.

An ant is one foot from the ceiling in the middle of the 12 foot long wall on the north end of the room.

A drop of honey is in the middle of the 12 foot long wall on the south end of the room, one foot from the floor.

How far does the ant have to walk to get the honey.

Hint: if the obvious path were the shortest, I wouldn’t have bothered to post the problem.

Have fun!

— Max

Thoughts on Oracle’s NoSQL offering

I’ve gotten a lot of questions from press, analysts, and customers about Oracle’s NoSQL offering. Our booth at Oracle Open World has been mobbed (next year we need a bigger booth – this year we had to make do with spilling over about 8 feet into the walkway on either side of our booth, sorry for the blockage for anyone trying to get past us!). I thought I’d share some further thoughts on Oracle’s now-announced offering here.

Disclaimer: I work for 10gen, the company that sponsors MongoDB, so I have some obvious bias. That said, I strongly believe that solid offerings from big players will help the market overall. With that bias disclosed, I have done my best to be fair and intellectually honest in my analysis of their offering.

About the offering

Personally, I think the Oracle offering is reasonable. Their approach to consistency looks sensible, as do their replication and sharding designs. It looks like it will be available open source, so I expect it will get a reasonable amount of adoption. I don’t think it breaks new ground, but if you want a key-value store from Oracle, it looks like it will do the job. My prediction is that it won’t crack the top 3 in NoSQL, but it looks solid and with Oracle behind it I’d expect it to wind up somewhere around # 5 or so in a very competitive market. This is just based on looking at their white papers; final judgement will have to wait until the product is released.

One plus for their offering is that it is based very heavily on BerkeleyDB. This technology has been around for at least 15 years, so it should be pretty stable. The main addition appears to be hash-based sharing; this is the part that customers need to ensure is stable before adopting it, but I’d expect the rest of it to be quite solid.

On criticism for flip-flopping

There have been a lot of harsh words about Oracle’s switch from writing a white paper on “Debunking the NoSQL Hype” in May to announcing a NoSQL offering in October. I wish it were otherwise, but welcome to the world of high-tech marketing. When a big company feels pain in the market and doesn’t have a product, they have their marketing guys write something that says the market isn’t important. You can be grumpy that the industry works that way and think whoever decided to do that is a hypocrite, but it really has no bearing on Oracle’s commitment to the product now that they have built it. Time to move on and evaluate the product on its merits.

So, congrats to Oracle on entering an exciting and growing market segment with what looks to be a solid offering. I look forward to seeing how it evolves over its next few releases and to competing with them in marketplace!

— Max

Oracle does NoSQL

Recently there have been rumors of Oracle introducing a NoSQL database at Open World next week. As a 9-year Oracle veteran as well as an 8-year veteran of the alternative database world (most recently as President of 10gen, the sponsor of MongoDB), this is an exciting development for me.

I don’t think NoSQL means the end of SQL or relational – its one of the reasons I don’t love the name “NoSQL”. I do, however, think that relational is not the answer to everything. When I left Oracle eight years ago to work on alternatives to relational database, I felt that there was space for an alternative that was more agile for developers and more scalable for deployment on a large number of commodity servers. The last eight years with the emergence of web 2.0 and cloud deployment have only strengthened my belief that relational is not the answer to all questions.

How do I feel about Oracle introducing a “NoSQL” database”? I think it makes all the sense in the world. Oracle already has acquired a variety of database products ranging from the acquisition of RDB from DEC to Sleepycat and TimesTen to MySQL (acquired with SUN). Much of the innovation in the database world right now is focused on scalable non-relational databases, most of which are open source and  which tend to be lumped under the “NoSQL” banner. The innovation is focused there for three reasons:
– Customers want horizontal scalability to support deployment on clusters of commodity servers, often in the cloud
– Customers want greater agility in their database to accomodate data whose structure is changing or heterogeneous
– Customers want easier development

In my opinion this is a good thing for alternative database vendors. Competition is already thriving in the sector and I don’t think one more competitor, even one as large as Oracle, will alter the  dynamics dramatically. But many customers will take Oracle’s arrival in the space as a sign that this trend is significant and it is a space they should look at. If Oracle’s offering is strong, we may lose some market share to them, but their presence will make it a bigger market.

In my time at Oracle, I found Larry Ellison to have a great sense of what markets were important and to be a fierce competitor. In some markets Oracle has crushed competitors (eg, RDBMS vs Sybase, Informix, and Ingres); in others it has struggled for a time and eventually succeeded through acquisition (eg, enterprise apps vs Peoplesoft, Siebel, and SAP); in some its presence has barely been felt (eg, SaaS vs Salesforce and NetSuite). How will Oracle’s entry into the NoSQL market fare? I don’t know, but I’d love to hear your thoughts.

Oracle, welcome to what in my opinion is the most exciting part of the database market!

— Max

My nominee for the worst bartender ever

It is not often that service is bad enough to be worth writing about. Tonight’s bartender in London was something special.

After dinner a few of us ordered drinks in the hotel bar. The menu was somewhat limited (after hours room service menu), but one of the cocktails they offered was a Martini. The only Gin they had was Tanqueray.

I ordered a Tanqueray Martini, straight up, with olives. Not particularly complex. They also had only one vodka; my colleague ordered an Absolut Martini with blue cheese olives. Surprised when he took the order I asked if they had blue cheese olives. He confirmed, and I asked to change my order to a Tanqueray Martini with blue cheese olives.

You are probably thinking that I am grumpy that I didn’t get my blue cheese olives. If only that was the biggest problem with my order. Even if I’d gotten a Martini on the rocks with regular olives, it wouldn’t have been that noteworthy.

20 minutes later, however, what arrived was lukewarm, had no olives, and didn’t smell like gin. It also wasn’t quite clear, slightly yellowish. After a bit of conversation we determined that what we’d gotten were two glass of warm vermouth. When we said we didn’t want them, he said ok, but that we should pay anyway. He even brought out the bottle of Martini brand vermouth to support his case that he’d made us exactly what we asked for. Incredibly, all the discussion of olives, Tanqueray, and Absolut had been completely ignored, as had the traditional definition of a Martini.

Even if you have no idea how to make a Martini (in which case I you need to find a different line of work), what on earth is going through your head when there is all of this talk of Tanqueray and Absolute and blue cheese vs regular olives?

Giving up on getting a Martini, I ordered a Stella (primarily because I’d seen someone else get one correctly). My colleague ordered a Jameson’s and got a Jack Daniels.


— Max

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