## Puzzles Involving Number 17

17 the 7-th prime number and the only prime of the form p^q + q^p, where p and q are prime: 17 = 2^3 + 3^2

the first prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, …

17 is the only prime number that is the sum of four consecutive primes (2 + 3 + 5 + 7).

17 is the lowest number that can be written as A^3 + B^2 in 2 distinct ways:
17 = 2^3 + 3^2 and 17 = 1^3 + 4^2

17 is a Fermat prime and it is also the exponent of a Mersenne prime (a prime p for which 2^p – 1 is prime).

Puzzles :

(1) Why is a number of the form abcdefghabcdefgh is divisible by 17 (replace each letter with a digit. E.g. 1234567812345678)?

(2) The wallpaper groups are the 17 possible plane symmetry groups.

(3) The problem of the 17 camels : A sheik has 3 children and owns 17 camels. His will stipulates that the eldest is to receive half his property; the second son is to receive the third of his property; and the third one, the ninth of his property. On his death, how would the sons share out the inheritance?

(4) x and y are integers between 2 and 100. Alex knows S = x+y, and Pat knows P = xy, but they do not know x and y. “I can’t calculate them” Pat says, “I knew” Alex says. “So I know these two numbers” Pat says, “In this case, so do I” Alex concludes.

Solution?

(5) Autoreferential growth rate : an enterprise growing at the rate of exactly 17.65717% per year will become exactly 17.65717 times larger in exactly 17 years, seven months, 29 days, and 21 hours… Which is exactly 17.65717 years!

math grad - Interest: Number theory
This entry was posted in Culture and tagged , . Bookmark the permalink.

### 47 Responses to Puzzles Involving Number 17

1. johnny says:

like me

• It is best to participate in a contest for among the finest blogs on the web. I will advocate this web site!

• Delightful!

• Really funny. Loved the writing.

2. I’d come to bury the hatchet with you here. Which is not something I typically do! I really like reading a post that will make people think. Also, thanks for allowing me to comment!

3. I’d come to give blessing with you here. Which is not something I usually do! I enjoy reading a post that will make people think. Also, thanks for allowing me to speak my mind!

5. Just discovered this blog thru Google, what a pleasant shock!

6. news says:

I found your entry interesting do I’ve added a Trackback to it on my weblog and my seotons :)……

7. Hi! Your article rocks and is really a very good understand!…

9. mutuelle says:

Hi! Your article rocks and is really a very good understand!…

10. When are you going to post again? You really entertain a lot of people!

11. You should take part in a contest for one of the best blogs on the web. I will recommend this site!

12. You made some good points there.

13. I was looking in yahoo for something else, but I have to say your website is very interesting

14. Such a good article. Good job

15. I carry on listening to the news lecture about getting free online grant applications so I have been looking around for the most excellent site to get one. Could you tell me please, where could i acquire some?

16. Spot on with this write-up, I truly think this website needs much more consideration. I’ll probably be again to read much more, thanks for that info.

17. Can I just say what a relief to find someone who actually knows what theyre talking about on the internet. You definitely know how to bring an issue to light and make it important. More people need to read this and understand this side of the story. I cant believe youre not more popular because you definitely have the gift.

18. Rich Erholm says:

To be a pupil My organization is performing an investigation concerning debt help. We observed your web site i need to express I’d been extremely impresed. Cheers a good deal to your diligence.

19. Your place is valueble for me and my seotons. Thanks!…

20. Nice post. I was checking constantly this blog and I am impressed! Extremely helpful info specifically the last part I care for such info much. I was seeking this particular information for a long time. Thank you and best of luck.

21. Thank you for the auspicious writeup. It in fact was a amusement account it. Look advanced to far added agreeable from you! By the way, how can we communicate?

22. Hey is it okay if I link to you in my blogroll?

23. Great post. I will be bookmarking and sharing it with my social networks.

24. generika says:

What i find troublesome is to find a weblog that can capture me for a minute however your weblog is different. Bravo.

25. I really want to get my greasy paws on this! I can already feel my grades going down until I crack the game!

26. Its like you read my mind! You seem to know a lot about this, like you wrote the book in it or something. I think that you could do with a few pics to drive the message home a bit, but other than that, this is magnificent blog. A great read. I will definitely be back.

27. I’m right here to see the right comments! Err, this site won’t insert properly upon my Ipad.

28. Many interesting content. I would just like to know if your experience in this matter based on the theory and practice?

29. diät says:

Hey I was looking to use some of your information on my small german blog if that would be ok?

30. Thank you for the auspicious writeup. It in fact was a amusement account it. Look advanced to far added agreeable from you! By the way, how could we communicate?

31. angielski says:

Nice blog. Thank you for sharing body

32. When I originally commented I clicked the -Notify me when new comments are added- checkbox and now each time a comment is added I get four emails with the same comment. Is there any way you can remove me from that service? Thanks!

33. 80's music says:

I thought it was going to be some boring old post, but it really compensated for my time. I will post a link to this page on my blog. I am sure my visitors will find that very useful.

35. benvitalis says:

Thanks to all of you for the positive feedback.

36. This one is an inspiration personally to uncover out way more associated to this subject. I have to confess your data prolonged my sentiments as well as I’m going to right now take your feed to stay up to date on every coming weblog posts you may possibly create. You are worthy of thanks for a job perfectly executed!

37. This particular site is really wonderful as well as i definitely appreciate it! Great job!

38. e marketing says:

Great post! Thank you

39. Can I just say what a aid to seek out someone who actually knows what theyre talking about on the internet. You undoubtedly know the right way to convey an issue to light and make it important. More individuals must read this and understand this facet of the story. I cant imagine youre not more common since you undoubtedly have the gift.

40. I was at party and 48h without sleep, im pretty sure i was reading same article somewhere, if not Im sorry