## Answer to Charming Little Puzzle

Yesterday I posted a charming little puzzle. It is one of the types that you either see the answer immediately or you have to work on it a bit. The puzzle:

Where the A, B, and C are self-referential. That is, If the Answer is A, then the answer is “Answer A”

The puzzle is that this puzzle has one and only one correct answer. What is it?
The quickest way for me to see the answer was to start at the top. If A is correct, then B is also correct, but I said there was only one right answer, so it cannot be A. Similarly, if B is true, then C is true, but again there is only one correct answer. Therefore B is out. That leaves C. C can be correct if B is false. Problem solved.

But no good problem should be allowed to pass without an attempt at a generalization of the underlying structure. For instance, could this puzzle work it we added “D. Answer C or D”?

Can you formulate a similar puzzle with three choices as in “D. Answer B, C, or D”?

What about other Boolean operators? Could you formulate a similar puzzle based on “and” rather than “or”? Example: This puzzle has two correct answers…

## What is the Right Answer?

Too much pure decision theory gets boring.  That is why I like to intermix it with puzzles and games which are related in some way to decision making and logic.  But making up clever puzzles is difficult, and so I comb the Internet to find good examples.  Today I am taking a slight variation of one of the fine puzzles that can be found here.

The puzzle is deceptively simple.  And I like it because it is presented backward with answers first and question to follow.

where the A, B, and C are self-referential.  That is, If the Answer is A, then the answer is “Answer A.”  Is that confusing?

The puzzle is that this puzzle has one and only one correct answer.  What is it?

I will post the analysis tomorrow, but you can navigate to the originating site and find the analysis now if you are impatient.

The charm for me of this little gem is that either you see it immediately, or you have to work out the logic.  You can get the correct answer either way, but having that sudden flash of insight is special.

After you work it out, go back and look at the post on dice in which A beats B on the average, and B beats C on the average, and C beats A on the average.  How are these two puzzles different?

Answers to the two puzzles: (1) two bars — one a magnet, (2) sphere with a hole in it.

If you have not seen the post with two puzzles, I suggest you look at it first before seeing the answers.

Two bars: Since I read this one long ago, I do not remember how many answers Martin Gardener gave, but the obvious one is to take one of the bars and point the end at the middle of the other (at right angles). If you picked up the magnetized bar, it will attract the other one. If you picked up the un-magnetized bar, it will not be attracted. The bar magnet is a dipole. That is, like all magnets, it has a north and south pole at either end.

[Note: some smarties might suggest the rod had been magnetized cross-ways. They can get their own puzzles.]

However, there is a variety of alternate solutions without necessarily bending the conditions of the puzzle. For instance, one could reasonably expect to find a string somewhere in the room. Suspend one the bars by the middle and see if it is attracted to some direction (North or South, if you know where they are, but that is not necessary).

Can you think of other out-of-the-box solutions?

Hole in the sphere: This puzzle is cute for several reasons. First, it helps us to distinguish between solving a puzzle and proving the answer. These are different things. For instance, I could guess and maybe get the right answer. We have all done that on tests. In math class, proofs are supreme. In the outside world, getting the right answer is supreme and proofs are a tool to be sure you have the correct answer. For this puzzle, I only asked for the correct answer, and I gave you a clue of how to find it without proving your answer is correct — that is proving it without using my clue.

The essential clue is that you have enough information to solve the problem. There are three obvious parameters: the length of the hole, the diameter of the hole, and the radius of the sphere. Intuitively we realize they are related. A bigger radius means a larger diameter hole to keep the total length the same. But I said you only needed the length of the hole to solve the puzzle. Therefore a reasonable person can conclude that any radius and matching diameter will give the same answer. You can pick any value you want. Therefore pick a diameter of zero and the corresponding radius of 0.5 inch to give a total length of the zero-diameter hole of one inch.

The volume is simple that of a sphere of that radius v = (4/3)πr3 (should be r cubed). You would compute the same answer for first principles if the radius was given as two feet or a mile.

That is the answer. If you want to prove it, there are several methods. The brute force way is to look up the formulas for the volume of a sphere (above), a cylinder, and the two end caps. The desired volume of that of the sphere minus two end caps and minus the cylinder. Another approach is to write an analytical formula for the half-moon-like cross section (i.e. two-dimensional) and the use standard method to rotate it around the main axis. Either way, you get the same answer, but why trust me? Try it.

[Photo above by Mykl Roventine / CC BY-ND 2.0]

## \$3 Bill Lottery Karma

﻿Have you stopped by Lockergnome.net yet? In a nutshell, it’s a new site where you can ask and answer questions with fellow Gnomies and earn fabulous karma points!

Today’s random 10 questions posed at Lockergnome.net:

[Photo above by tj scenes / CC BY-ND 2.0]

## Ten Random Lockergnome.net Questions

﻿Have you stopped by Lockergnome.net yet? In a nutshell, it’s a new site where you can ask and answer questions with fellow Gnomies and earn fabulous karma points!

Today’s random 10 questions posed at Lockergnome.net:

[Photo above by Chris Pirillo / CC BY-ND 2.0]

## Gmail Blog – Choosing A Smart Password

The art of choosing a smart password has been lost for many who use the Internet. Some newbies assume that using their middle name, numbers from their home address, birth date, or other easy to remember password is enough to keep them safe. On the flip side we have those who use a complicated formula that is so complicated they can’t remember what the password is! Either way can be frustrating for the user when they attempt to access a web site or their own data.

Creating a new password is often one of the first recommendations you hear when trouble occurs. Even a great password can’t keep you from being scammed, but setting one that’s memorable for you and that’s hard for others to guess is a smart security practice since weak passwords can be easily guessed. Below are a few common problems we’ve seen in the past and suggestions for making your passwords stronger.

Problem 1: Re-using passwords across websites
With a constantly growing list of services that require a password (email, online banking, social networking, and shopping websites — just to name a few), it’s no wonder that many people simply use the same password across a variety of accounts. This is risky: if someone figures out your password for one service, that person could potentially gain access to your private email, address information, and even your money.

It’s a good idea to use unique passwords for your accounts, expecially important accounts like email and online banking. When you create a password for a site, you might think of a phrase you associate with the site and use an abbreviation or variation of that phrase as your password — just don’t use the actual words of the site. If it’s a long phrase, you can take the first letter of each word. To make this word or phrase more secure, try making some letters uppercase, and swap out some letters with numbers or symbols. As an example, the phrase for your banking website could be “How much money do I have?” and the password could be “#m\$d1H4ve?” (Note: since we’re using them here, please don’t adopt any of the example passwords in this post for yourself.)

Problem 2: Using common passwords or words found in the dictionary
Common passwords include simple words or phrases like “password” or “letmein,” keyboard patterns such as “qwerty” or “qazwsx,” or sequential patterns such as “abcd1234.” Using a simple password or any word you can find in the dictionary makes it easier for a would-be hijacker to gain access to your personal information.

Solution 2: Use a password with a mix of letters, numbers, and symbols
There are only 26^8 possible permutations for an 8-character password that uses just lowercase letters, while there are 94^8 possible permutations for an 8-character password that uses a combination of mixed-case letters, numbers, and symbols. That’s over 6 quadrillion more possible variations for a mixed password, which makes it that much harder for anyone to guess or crack.

Problem 3: Using passwords based on personal data
We all share information about ourselves with our friends and coworkers. The names of your spouse, children, or pets aren’t usually all that secret, so it doesn’t make sense to use them as your passwords. You should also stay away from birth dates, phone numbers, or addresses.

Solution 3: Create a password that’s hard for others to guess
Choose a combination of letters, numbers, or symbols to create a unique password that’s unrelated to your personal information. Or, select a random word or phrase, and insert letters and numbers into the beginning, middle, and end to make it extra difficult to guess (such as “[email protected]”).

Problem 4: Writing down your password and storing it in an unsecured place
Some of us have enough online accounts that we may need to write our passwords down somewhere, at least until we’ve learned them well.

Solution 4: Keep your password reminders in a secret place that isn’t easily visible
Don’t leave notes with your passwords to various sites on your computer or desk. People who walk by can easily steal this information and use it to compromise your account. Also, if you decide to save your passwords in a file on your computer, create a unique name for the file so people don’t know what’s inside. Avoid naming the file “my passwords” or something else obvious.

Solution 5: Make sure your password recovery options are up-to-date and secure
You should always make sure you have an up-to-date email address on file for each account you have, so that if you need to send a password reset email it goes to the right place.

Many websites will ask you to choose a question to verify your identity if you ever forget your password. If you’re able to create your own question, try to come up with a question that has an answer only you would know. The answer shouldn’t be something that someone can guess by scanning information you’ve posted online in social networking profiles, blogs, and other places.

If you’re asked to choose a question from a list of options, such as the city where you were born, you should be aware that these questions are likely to be less secure. Try to find a way to make your answer unique — you can do this by using some of the tips above, or by creating a convention where you always add a symbol after the 2nd character in the answer (e.g. [email protected]) — so that even if someone guesses the answer, they won’t know how to enter it properly.

What secret formula do you to produce a password that you believe is secure? Share your thoughts with us.

When Google announced that it would be introducing its Chrome Operating System next year, it was only a matter of time before questions arose. The Google Chrome Blog team immediately set out to answer some of the most popular questions.

Yes – Google Chrome OS is an open source project and will be available to use at no cost.

The Google Chrome OS team is currently working with a number of technology companies to design and build devices that deliver an extraordinary end user experience. Among others, these companies include: Acer, Adobe, ASUS, Freescale, Hewlett-Packard, Lenovo, Qualcomm, Texas Instruments.

I’m a developer – how can I work with you?

Thanks for your interest. Later this year, the Google Chrome OS code will be open source. We’re looking forward to working with the open source community and making our own small contributions to the great work being done out there. Please stay tuned.
But while  visiting the Google Chrome Blog brought up another thought. I find it interesting that Google chose the same name for its browser as it did for its upcoming operating system. Could this mean that its browser will actually be the operating system?

What do you think?

## Since I’m A Smart Alec, Let Me Google That For You

Gnomie Stuart Ferguson from Glasgow, Scotland writes:

Hey Chris,

Have you ever been asked a question that you have been reluctant to answer because the person asking could have easily just “googled it?” Well here is a Web site that I think you may find quite fun: Let Me Google That For You.

When you enter this Web site you can type whatever question you wish into the search box then click search. What this will do is give you a link that, when clicked, will play a short animation of a cursor on a Google page moving to the search box then typing out whatever question you typed before redirecting to an actual Google search of that question. You send this link to whoever asked the question.

This should be a fun alternative to simply saying “GOOGLE IT!”

Thanks for your time, Chris. I’m an avid watcher of your YouTube videos and you have showed me so many cool things in the past.