If you would like to learn more about me or contact me, you can find the information of my webpage: http://www.tanyakhovanova.com

Try also my pet project: http://www.numbergossip.com

I am thankful to Sue Katz who did most of the editing for this blog. Other people who helped me with English are:  Alexey Radul, Sergei Bernstein, Rebecca Frankel and Hillary Holloway.

1. #### Sue:

Tanya, The new layout looks fabulous and your blog continues to be both unique and witty. Congratulations,
Sue

2. #### Des Wann:

Congratulations, Tanya!! Love your website. Hopefully, if time permits, I will study carefully your many and varied choices. As a retired Chairman of a Mathematics Department I might also be able to make contributions to these items.
Des

3. #### Robin Whitty:

A lovely collection! It is so nice of you to fulfill your duties as Prof. of Recreational Mathematics even before anyone has the good sense to pay you for it! Good luck with the job hunt and the blog in 2009!

Robin

4. #### Jack Wert:

Subject: 12 coin “counterdeit coin” problem
Tanya: Have you seen my solution to this problem
It is very simple and, as the mathematicians say, “recursive” - whatever that means.
Her is is:
Divide the coins int three main groups of 4 coins eacn
Divide each of these into sub groups of 3 and 1 coins
Place two main groups on the pans of a two pan balance and the third on the table
Observe the condition of the balance.
Rotate the groups of 3 coins (pan A to pan B) (pan B to table) (table to Pan A)
Observe condition of balance.
If there is a change, it will indicate which group of 3 containss the odd coin and its relative weight.
In this case, discard all other coins and divide this group into single coins, placing one on each pan
balance pan and one on the table. This will identify the odd coin. Problem solved.

If ther is no change, discard the groups of 3 and place the rotate the single coins. This will
identify the odd coin. Problem solved.

5. #### Dave Marain:

Tanya,
It is an honor for me to be included on your blogroll. Your site/blog is witty, stimulating and truly unique, a reflection, I suspect, of its author! I wish you only the best in your personal and professional life. Sergei is a lucky boy indeed…

BTW, IMO, I believe that it is not coincidental that left-brained mathphiles are usually languagephiles. I enjoy your linguistic puzzles as much as your math challenges perhaps because languages are essentially based on code and that appeals to my inner cryptologist! Now ask Sergei to determine the sum of all 7-digit palindromes each of which contains the 4 prime digits.
Dave

6. #### Dave Marain:

Tanya,
I should mention that Sergei has only 60 seconds to solve the palindrome problem mentally (no paper, writing implement or electronic device)!
Dave

7. #### Doug:

I really enjoy this blog. I actually believed i had a pretty good intuition for math until i began reading this blog. Keep up the excellent work!

8. #### Arvald Karp:

Hi Tanya,

I’ve learned of your blog through Misha Livshits, the guy who invented calculus without limits. He mentioned you are into new ideas for start-ups. I was wondering if we connect sometime and chat.

Hope you are having a good week.

Cheers,
Arvald Karp

9. #### arveen panda:

Hey Tanya,

Your blog is a very refreshing !!! You are awesome! God Bless You

Cheers
Arveen Panda

cool blog.

11. #### Pratik Poddar:

Nice blog.

Thanx a ton for the awesome blog.

Regards,
Pratik

12. #### Animesh Saxena:

I loved reading your blog. I am an analyst at an investment bank, who uses mathematics extensively for derivative products. I enjoy reading anything related to maths. The jackpot post was too good!

13. #### Xamuel:

Hi Tanya, I also write a lot about math, and I did a double-take when I clicked your site from Google and saw we use the same theme What is it about fluid-blue that appeals to mathematical minds.. *grin* Anyway, you’ve got yourself a new reader

14. #### Pratik Poddar:

Mam,

Can I ask why does number gossip support only numbers till 9999. Is there some reason to do it? I believe the properties are determined and displayed on the fly right? You could do it for larger numbers.

15. #### Tanya Khovanova:

Pratik,

Some of the properties are precalculated and stored in files. The program that generates them is too slow.

16. #### Sally Friedman:

Dear Ms. Khovanova:

I enjoy reading your blog, and was wondering if you would like to do a link exchange. My book blog’s url is educationanddeconstruction.com. Every week, I make a nonfiction book recommendation in the topic areas of education, history, technology, biography and/or humor. I have already put up your link. Please reply if you would like to do a link exchange. Thank you.

Sincerely,

Sally Friedman

17. #### Top 50 Inspiring and Educational Ph.D. Blogs:

[…] Tanya Khovanova’s Math Blog: Information on math, life as a mathematician and more. […]

good blog

19. #### Francisco:

Hello
We are Francisco Ormazabal and Jorge Diaz, we are studying mathematic and computation pedagogy at Universidad Catolica del Maule.
Checking the blog we are have found an excellent work, a blog with many types of themes in relation to mathematic.
You can appreciate that there is a lot of preoccupation about the users that visit the blog.
To keep up to day the blog with diverse themes, as users, it is something that satisfies us and makes us to want to keep visiting.
We had checked others blogs in relation to our career, but we realized that they were not up graded, such as in the themes and in the users posts.
What really impressed us from this blogs was the puzzles part, because it is very funny to learn mathematic in this way.
Congratulation

20. #### diLLa:

heloo
can you tell me..
about application differentiation in daily life….
what is deriative??

can you asnwer my question??

LOVE IT

22. #### Rich Bauer:

Your blog is unusual in that you publish theorems and interviews of interesting people. The diversity is stimulating and the light-hearted style makes reading you fun. Thanks!

love it…

24. #### James Harris:

Just came across your site. Here’s a question: what controls the size of integer solutions to x^2 - Dy^2 = 1?

The answer in general (there are trivial identity cases) is the number of prime factors of D-1. If D-1 has a lot of small prime factors then integer solutions for x and y must be very large in comparison to when D-1 is prime. Notice you can approach that out as well by using (n-m)^2 - Dm^2 = 1, and considering mod D-1.

n^2 - 2nm + m^2 - Dm^2 = 1, so n^2 - 2nm - 1 = (D-1)m^2, so n^2 - 2nm - 1 = 0 mod D-1

Notice n is blocked from having prime factors in common with D-1, and also note that n = x+y or n = x-y from the traditional equation.

Fun!!!

25. #### David Brooks:

I’m looking for some info you might be able to help me with. 998001 is an interesting number. Its inverse (1/998001) is a repeating decimal with a period of 2997.

It starts out 0.000 001 002 003 004 005 … and continues counting until it gets to 997. Then it skips 998, does 999, and starts to repeat itself.

I was wondering if they have a name this this kind of integer - an integer whose reciprocal or inverse produces a decimal that shows a known or familiar sequence of numbers. This one counts natural numbers. But I have found others that count by even numbers, powers of 2, and Fibonacci numbers.

I would like to know if anyone has already researched these, or if I might have started on something new in mathematics.

Any info you have would be helpful.

Thanks,

26. #### Simon Jensen:

Hi! Thank you for your wonderful website. I enjoy it!

I wrote this “paradox” a couple of years ago, and I would like you to have a look: http://blogoff.simonjensen.com/#post4

Also, this one is quite funny. I have only met a few person who could see the solution at once: http://blogoff.simonjensen.com/#post0

Best regards,
Simon Jensen

27. #### Art DuPre':

Dear Tanya,
I fist noticed your website when I ran across David Wilsons “Divisibility by 7 is a walk on a tree”, which seemed pretty mysterious, and I REALLY noticed when his “Divisibility by 7 is a walk on a tree II” , which removed the mystery. I replaced the white arrows with “inside arrows”, and have been teaching it to my finite math students at Rider and TCNJ, both of which are “terminal” math courses. Sounds like a disease, right? As you know, it merely means that I do not have to prepare them for a subsequent math course, so I have a pretty free hand.
I think I heard your ex talk in Gelfand’s seminar at Rutgers. I was certainly aware of him.
It has been 39 years since I translated Klein-Fricke(Elliptic Modular Functions) and Fricke-Klein(Automorphic Functions) into english(2800 pages in all). I was never published, so I am going to put it into PDF form and publish it on the web.
You relly have an impressive set of math pages, and it’s enjoyable reading them Keep up th good work.
Is David Wilson the same as the ex graduate at Rutgers by that name?
I talk a lot with Doron Zeilberger. Do you know MIchael Somos, of Somos sequence fame?

Art

28. #### Art DuPre':

Here’s a paradox I created decades ago, but have not seen it elasewhere.

“This sentence does not refer to itself”

29. #### laila naji:

I want to ask you about the theorm and it’sprrov for why grreaco latin square not exsit in n=6

,please tell me to day.

30. #### Bharath:

Hi Tanya

Would like to connect with you regarding a math educational game. mathtrail.heymath.com is the link to access the game.

Thanks and looking forward to connect with you.

Regards
Bharath