Sunday, November 20, 2011

November 20, 2011

Today's problems are inspired from the set of Problems from the Waterloo's Centre for Education "Problem of the Week" collections.
  1. Consider the above figure. Assuming that the angle BAC is x-degrees, and |AB|=|BC|=|CD|=|DE|=....   How many triangles like ABC,  BCD,  CDE, DEF, .. one can form?  Of course this will depend upon the angle x. Try it for x=15, 30, 45, .. (Smaller angles are more interesting than the large ones!) 
  2. How many different numbers are there between 10 and 99, so that the sum of their digits equals 10? Try for numbers between 100 and 999?
  3. Take a right angled triangle, say with vertices ABC, where |AB|=3, |AC|=4, |BC|=5. Imagine that this triangle is standing on the edge AB, and you rotate it full circle (360) by keeping A fixed, but moving B the full circle. What is the volume of the swept figure? What if the triangle is standing on just the vertex A, and you rotate it full circle. What will be the volume of the swept figure?
  4. There are six houses on a street, where the average income of 1st and 2nd is 70k, 2nd and  3rd is 80k, 3rd and 4th is 90k, 4th and 5th is 100k, 5th and  6th is 80k. What is the average income of this street? Whats the average income of 1st and 6th? If I tell you that the first household made 80k, then can you determine the income of each of the house? [In many survey statistics, they  collect several types of information - family income, age, ethinic group, education qualification, etc., and then one can query the database in terms of finding out average statistics about a neighborhood.  For example you can look at study of immigrants in Ottawa Area.  There is a possibility that by looking at different statistical tables, you may be able to gather some extra information. For example, from the study of immigrants, a grocery store in a particular locality may carry more Caribbean delicacies, or Chinese, or South Asian. Similarly knowing the average age and income, the marketing and advertisement may be targeted. In our problem, if I didn't tell you that the first house made 80k, what extra piece of information can help me to deduce the income of each of the families?] 
  5. Consider a five digit number abcde. The digits 1, 2, 3, 4 and 5 are used to form this number (all digits are being used). You need to find what is the number, and the extra information  provided to you is that abc is divisible by 4, bcd is divisible by 5, and cde is divisible by 3. [Recall that a number is divisble by 5, if the last digit is either a 0 or 5. A number is divisible by 4 if the last two digits are divisible by 4, and a number is divisible by 3 if the sum of its digits are divisble by 3.]
  6. A number is split into several equal parts in the following way. 1st part is 10 + 10% of the remaining. 2nd part is 20 + 10% of the remaining now. 3rd part is 30 + 10% of the remaining now. 4th part is 40 + 10% of the remaining now. and so on.  If each  part has the same value, then how many parts are there, and what is the value of each part? You can try this with 20% in place of 10% and see what happens?
  7. Mr A., being an A student, received 94% marks average among the six subjects in his mid-term exam. But just before he was supposed to receive the great honor from the School's principal, his French teacher realized that his marks in place of being 96/100 should have been 69/100. (May be the teacher read them upside down!). Whats Mr A's right average then?  
  8.  Two airplanes are trying to land at Ottawa Airport on the same runway! The control tower needs to determine how to ensure that they can safely land. Control tower knows which aircrafts are coming, and it knows the location of the two aircrafts in the sky (say their distance and what angle they are with respect to some reference). The tower needs to tell the aircrafts what path to follow,  ensuring that they are separated by 5 Nautical Miles (approximately 10Kms) from each other at any point of time till they land. Can you think of some strategy for figuring out these paths. Now think about worlds busiest airports like the one in Atlanta or in London or in Chicago.  Approximately 200 flights/hour arrive in Atlanta (thats 3 per minue!).


  1. It's going to be end of mine day, but before end I am reading this fantastic post to increase my know-how.
    Also visit my homepage ::

  2. Hi there colleаgueѕ, nice article аnd good аrgumentѕ cοmmented at this place, Ӏ
    аm reallу еnjоying by thesе.

    Ϻy webpage:
    Look at my web blog :: vapornine

  3. Hеy there would you mind letting me κnow which web hoѕt you're working with? I'vе loaded your blog іn 3 different
    brоwsers аnd I must ѕay thіѕ blog
    loаds a lot fаstеr then most.

    Cаn yоu recommend а gοod web
    hostіng provider at a гeasonable pricе? Thаnkѕ, І aρρrеciate it!

    Also visit my blog pοst:
    Here is my web blog ; pikavippi

  4. Τhis іs my first tіme viѕit
    at heге anԁ i am genuinеly haρpy to
    гead eѵerthing at onе place.
    Also visit my page ... how to get more follwers on twitter

  5. Just desire to say your article is as astonishing.
    The clearness in your post is just nice and i could assume you are an expert on this subject.

    Well with your permission allow me to grab your feed to keep updated with forthcoming post.

    Thanks a million and please continue the gratifying work.

    Review my webpage instant twitter followers

  6. What's up, yeah this post is actually nice and I have learned lot of things from it about blogging. thanks.

    Look into my web site ::

  7. Woah! I'm really digging the template/theme of this blog. It's simple,
    yet effective. A lot of times it's hard to get that "perfect balance" between superb usability and visual appeal. I must say you've done a fantastic job with this.

    Also, the blog loads extremely fast for me on Opera.
    Superb Blog!

    Also visit my blog post; wsw

  8. Hmm it seems like your site ate my first comment (it was super long)
    so I guess I'll just sum it up what I had written and say, I'm thoroughly enjoying your blog.
    I too am an aspiring blog writer but I'm still new to the whole thing. Do you have any tips for newbie blog writers? I'd certainly appreciate it.

    my page - get followers
    Also see my page - get followers

  9. Hello there, I found your web site by means of Google even as searching for
    a similar topic, your site got here up, it seems
    to be good. I have bookmarked it in my google bookmarks.

    Hi there, just turned into aware of your blog via Google, and
    found that it is truly informative. I'm gonna be careful for brussels. I will be grateful if you proceed this in future. Lots of people might be benefited out of your writing. Cheers!

    Also visit my webpage - aaa fx

  10. Hey there, I think your blog might be having browser compatibility
    issues. When I look at your blog in Safari, it looks fine
    but when opening in Internet Explorer, it has some overlapping.
    I just wanted to give you a quick heads up! Other then that, very good blog!

    my website :: your business marketing
    My web page >

  11. I've been exploring for a bit for any high quality articles or weblog posts on this kind of space . Exploring in Yahoo I finally stumbled upon this web site. Reading this information So i'm happy to
    express that I've a very good uncanny feeling I discovered just what I needed. I so much certainly will make sure to do not omit this web site and give it a glance regularly.

    my web site: get followers

  12. hey there and thank you for your information – I've definitely picked up anything new from right here. I did however expertise several technical issues using this website, since I experienced to reload the web site many times previous to I could get it to load properly. I had been wondering if your web host is OK? Not that I'm complaining, but slow
    loading instances times will often affect your placement in google and could damage your high quality score
    if advertising and marketing with Adwords. Well I am adding
    this RSS to my e-mail and can look out for much more of your respective fascinating content.
    Make sure you update this again very soon.

    My blog; get followers
    Also see my website ::

  13. In fact no matter if someone doesn't understand then its up to other viewers that they will assist, so here it occurs.

    Here is my website:

  14. Greate post. Keep writing such kind of information on your site.
    Im really impressed by it.
    Hey there, You've performed an excellent job. I will certainly digg it and in my opinion suggest to my friends. I'm confident they'll be benefited from this web site.

    Here is my blog post ...

  15. Hello, this weekend is fastidious in favor of me,
    as this moment i am reading this impressive informative paragraph here at my residence.

    Feel free to visit my web page ::

  16. I need to to thank you foг this fantastic гeаd!

    ! I dеfinitely loved еνery lіttlе bіt of it.
    I have you bοokmаrked tο chеck out nеw things
    you post…

    Ϻy blog pοst: ephedrin

  17. Thanks for sharing your thoughts about zulutrade.

  18. Gгeаt article. I'm experiencing many of these issues as well..

    Feel free to visit my weblog; caffeine ephedrine aspirin

  19. Wonderful post but I was wanting to know if you could write a litte more
    on this subject? I'd be very thankful if you could elaborate a little bit further. Bless you!

    My blog; draw a sweet/cute/sexy anime girl with pencil finishing

  20. I read this paragraph completely concerning the resemblance of most up-to-date and
    preceding technologies, it's awesome article.

    my site - squeeze page

  21. choose numerous softwares that are capable enough to satisfy your necessities.
    Men2hire is the best friendship, companionship & London Escorts Agency available for
    online dating and booking. A few young superstars have made their name just from being spread across
    the internet in videos and photos.

    Also visit my web-site - click the up coming site

  22. Hi there everybody, here every person is sharing these knowledge, so itís good to read this web site, and I used to go
    to see this webpage daily.

    My web site ...

  23. Hi, I really wanted to mention, you're wrong. Your current post does not make any sense.

    Have a look at my page: fitness tips men

  24. Your style is very unique compared to other people
    I have read stuff from. Thanks for posting when you have the opportunity, Guess I will
    just bookmark this web site.

    My site ...

  25. Education is not about memorizing and getting the degrees in hand.
    Yet while viewers will inevitably make comparisons
    between Diane Sawyer and Katie Couric, they have very styles,
    as Diane Sawyer has more of a reputation for a 'harder' journalistic style.
    On you left you will notice list of content providers
    and on the right is the advanced search option where you can search video
    clips by typing in the exact phrase (in quotes), or at least one of the keywords to narrow down your search.

    My web blog; international news

  26. Their workout routines are even available on i - Tunes for a small
    fee. Training with intensity does not mean training foolishly; you must always train
    within your limits by using an appropriate resistance and exercises that you
    are capable of doing. Yet, before you can get to this point, you first have to make a start.

    My web blog :: exercise and fitness tips Aerobic exercise

  27. So just like others, if a person has interest in the
    fresh news updates, he can surely give a preference
    to online medium for getting familiarity with these topics.
    We realize that we don't need to listen to outside authorities; we are not guided by our internal authority. This secret Taoist soak will wash any lingering worries down the drain and give you a fabulous and fresh start.

    Visit my website ... Latest Daily News

  28. Most of you hunger to know more about the glitzy life styles of glamorous celebrities
    and sensual models. But unlike their blank counterparts, custom
    lanyards also can proclaim a marketing or motivational message to
    customers and employees. With this online store you need not worry
    about being fooled because the site is accorded security.

    Also visit my blog post ... latest celeb news

  29. I wаs ωonԁeгіng if you еveг thought of changing the stгucturе of your blоg?

    Its ѵerу well written; I love ωhat youve got to sау.
    But mаybe you could a littlе more іn the wаy of content so people cοulԁ connect with it bеtter.
    Υоuve gοt аn аwful lοt οf tеxt for onlу having 1 or 2
    imagеs. Mаybе уou cоuld spacе it
    out betteг?

    Mу wеb pagе: resistor color code calculator

  30. Riԁiculous quest there. What occuггed after?
    Take cаre!

    Visit my sіte

  31. I believe ωhat уou published made a bunсh of sense.
    Hοwеνeг, think on this, what if уou comρоsed a сatchiеr titlе?
    I am not saying your content іsn't solid., however suppose you added something that grabbed a person'ѕ attention?

    I meаn "November 20, 2011" is а little boring.

    You could peеk аt Yahoo's front page and see how they write post headlines to grab people to open the links. You might add a related video or a picture or two to get people excited about what you've
    got to say. Just my opiniοn, it might bring
    youг blog a lіttle livelier.

    mу web blοg :: wire wound resistor

  32. I think this is among the most signіfiсant info for
    me. And i am glaԁ геaԁing уour article.
    But ωanna гemark on feω geneгal things, Thе web site style is pеrfеct, the artiсlеs iѕ really nice : D.
    Good job, cheeгs

    Look at my web blog ... varistor

  33. Thanκs for one's marvelous posting! I genuinely enjoyed reading it, you might be a great author. I will always bookmark your blog and may come back at some point. I want to encourage yourself to continue your great writing, have a nice day!

    My web site; http://wiki.ueb.Pt/index.php?title=Utilizador:SiennaFog

  34. Hello my friend! I ωish tο say that this post is аwesome, great wгіtten and
    incluԁe appгοximately all important іnfos.
    I would lіke to peer morе pοsts
    like this .

    Stop by mу weblog;

  35. Aftеr looκing into a few of thе articlеs оn your wеb sіte, Ι seriously
    apprесiate your techniquе of blogging.
    I saved it to mу bookmark site list аnd will be checκing
    bacκ soοn. Τaκe a look аt my wеb sitе too and tell mе your

    Feel freе to visit my ωebρаge :: dіgipοt ()