Thursday, May 14, 2009

A Math question for you.(Blog marathon Post 10)

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Mathematics--it either terrifies you or makes you ecstatic. You either like it or hate it. Somehow with Math, there are usually no middle paths.

Many people even fear it and I know some of my friends who still get nightmares about themselves being in the examination hall and not knowing a thing on the Math paper, even twenty years after they have left school! Such is the impact of the subject.

I like Math. But the last Math exam I gave was ages and ages back. I got a chance to relive that vicariously as my son has his Math papers tomorrow and day-after tomorrow at a National level examination. He too likes Math and so we have fun revising together and going over the concepts together.
What I really like about the U.K is their approach to education. In India, the Math teachers usually never make it fun. Also the schools really do not encourage any fun activities connected to Math. Here they have so many activities to make it interesting and now with the reach and penetration if Internet and Multimedia, the way they do it terrific. (If you have a child in the school going age you may find this site useful) Look at this activity for instance on Mental Math, which is from the BBC site.



What fun! They have activities like these for every topic at my son's level. For Median,Mode,Averages, Decimals, Percentages, Fractions, Probability, Co-ordinates,Data-interpretation (yeah they do all this at his level. He is 11)--you name it, there is a fun activity, revision bite and a quiz which you can do.

I am giving you a question from a previous year's question paper, that we had fun solving today. In case you don't get the answer (I am quite sure you will--but sometimes it just doesn't strike you) I shall give it to you as an addendum, after hearing what everyone has to say.

Here is the question:

The numbers in this sequence increase by 7 each time.
1,8,15,22,29..................

The sequence continues in the same way.
Will the number 777 be in the sequence? Explain how you know.

Please remember that you are NOT allowed to use equations to explain it, as they have not yet been taught any kind of equations at their level. So you cannot use terms like n, or x etc--as the children will not understand it. How will you explain your answer?

I will update this post tomorrow, giving you the names of two people who explain it best.[Remember I am looking for the best explanations that I think would appeal to a child of that age. So keep your explanations simple and clear. No point copying. Be original and as creative as you can,but relevant too :-) *Don't I sound like a real Judge in a TV contest? Have laid the parameters based on which I will pick the best two* :-)]

Let's see how good a Math teacher you will make!
Go!!
***********************************************************
Update as promised:

Oh My God! What an overwhelming response! And what wonderful explanations. It was really hard to pick whose explanation was the best. So I did a smart thing and delegated the task to one of my closest friends (who arrived from India today with her two children--she will spend a week with me) and to my husband. Both of them sat and read through all the responses. Then they came up with several categories like you see in the beauty contests (Miss. Beautiful hair, Miss, Beautiful skin etc) Based completely on their inputs (therefore my personal bias does not come in) here are the final winners *Drum rolls* *Trumpets* *Curtains rise*

The Bill Cosby award for the most humouros (and misleading) comment goes to

Ramesh of Business Musings.
(He writes a remarkably good business blog and he updates every day with relevant, useful topics, which have behind them the weight of his experience at very senior levels in leading Multinationals)


The Ramanujam award for Mathematical brilliance and for sheer perseverance and interest shown in this post goes to

Ajay Chauhan (He doesn't have a blog--so linked his orkut profile, but he has a great sense of humour and writing comes easily to him. If he starts a blog he will have a great following for sure. ( provided he does not decide to dazzle us all with his math abilities :P He not only answered this question but also answered the question posed by anonymous brilliantly. (I don't know why anonymous is hiding though )


The Manoj Kumar award for patriotism for bringing in the 'Mera Bharath Mahaan' angle to Math, goes to

Prateek Gupta of Ginger and Cardamom
(He was one of the first people who agreed to do the blog marathon with me when I was still dilly dallying and testing waters. He was also recently mentioned in the Pune Mirror as one of the most interesting twitterers in the City)


The Early bird award for right response goes to

Vinoo John of Vinoo
(She too is a participant in the blog marathon. She also went to college with me and we go back a long way. Her explanation was good too)

The true blue Mommy award (as she was the only one who actually put the question to her seven year old) goes to

Geetha
(she does not have a blog and I am not sure if she would like me to link her orkut profile. She has been one of my most loyal readers and is sensitive, warm and kind)

The most simple and Child friendly explanation award goes to

Aadi of 'The God particle'
I don't know him at all and I think it is the first time he has commented on my blog. He was the only one who used figures to explain it.

Thank you to all who explained! I am sure you will agree like true sportsmen that the joy was in the ride not the destination, because we all got there, didn't we? And the post did make you think, didn't it?


51 comments:

  1. Well Preeti, you made me use my rusted brain before going to bed!
    Answer is "NO"...777 is divisible by 7.. every number in sequence is one more than a multiple of seven! so 778 will be in the sequence!

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  2. cool....this is awesome...I have always liked math and it sure is fun...but only if you have a liking for it;-)
    As for the answer to u r math question...
    No 777 cannot be in the series! Any number in the series (minus) "1" should be divisible by "7". Like 29-1=28, 22-1=21 etc which is divisible by 7. 777-1=776 which is not divisible by 7!!
    Had fun doing it;-)!!!!

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  3. Couldn't resist :P :)

    Answer is - No, 777 won't be a part of the sequence because all numbers in the sequence are one (1) greater than a multiple of 7. So, as already mentioned by people above me, 778 would be in the sequence since it's 1 greater than 777 (which is a multiple of 7)

    The Calvin and Hobbes strip was an eye-opener :)

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  6. Hi P.S,

    HONESTLY this explaination is not mine..Its from my son(he is 7 yrs old)..I showed the sequence to him and he told immediately that 777 cannot be in the sequence..778 will be there though!!If the sequence had started with a zero the number 777 would be there, he told:)

    Beats me :(
    Had fun though because he explained it to me with great patience:)

    G.

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  7. Oh Forgot to add this..I still get nightmares like the ones you mentioned..But instead of Math its CHEMISTRY..:(..In those nightmares,I would have prepared for English or something..but actually its Chemistry..Ha..!!What a relief it is to wake upto reality:))

    G.

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  8. Oh Oh - all the nice people who have commented, and who will comment are all wrong. 777 does come in this sequence. You see, there is 1 captain, 8 air hostesses, 15 seats in first class , 22 dials in the cockpit,...... in a Boeing 777 aircraft. Can I now get a toffee please ?

    Incidentally, I completely agree on some of the great things in British schools. My daughter goes to one, here in China. But sometimes, they are nutty. She's 8 and is currently learning the difference between a farthingale, a parlet and a dumbroll in the Tudor period. And No, I am not explaining that !

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  9. The simplest way to put is == NO
    as the series has started with 1 we will not be have 777 in the series as 777 is divisible by 7 and the number mentioned in the series not divisible by , so NO

    and if you wanted a YES, then :) start the series with (0 7 14 ...) as in this case all number are divisible by 7 we will be having 777 in this series.

    /Anish

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  10. helllooo...even tho every1 before has pretty much answered it the way i want to...i couldn resist!!

    No 777 will not be in the sequence. Each no in the sequence is 1+(any no divisible by 7) for example 15 which is (1+14) and 14 is divisible by 7, hence by that logic, (1+777) or (1+770) would be in the sequence but 777 which is wholly divisible by 7 wouldnt.. :)

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  11. ohh and that activity in mental math is soooo kool!! :)

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  12. lol at Ramesh's comment...:D

    all the best to atul :)

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  13. I did not even give it a try, Preeti.. cos I am sure I will get nightmares! :) :)
    I love the Calvin and Hobbes strip.. Maths and Chemistry - for me, its an unethical religion! ;)

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  14. I am going Bonkers!!!...u can call me a Math Atheist....I am really bad wid numbers...Calvin n Hobbes...I love reading the comic strips..

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  15. Hi PS, this is the first time i'm commenting on ur blogs....but to be honest i love all ur posts,they give u such a happy feeling and bring a big grin on the face,talking bout math-till date i get math anxiety, i tried the game posted on ur article , but the anxiety makes it so difficult to solve even simple things.I'm mathphobic.

    Keep writing....ur marathon post is a treat for me:)....every morning there is sumthing fun and nice to look forward to i.e ur blog:)

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  16. I also love maths :)
    Unfortunately the answers are already explained by so many people.. It'll be a repeat.. Let me blame the timezone :)

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  17. The basic premise of all numbers from 1 increasing by seven makes it obvious that multiples of 7 would not appear in the sequence. Hence 777 would not appear in the sequence because it is a multiple of 7. :-)

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  18. I had jumped straight to comment form and then checked everyone else' comment ... Looks like you are gonna have to read the same explanation over and over ;)But it was good fun though ... I always loved Mathematics inspite of being an average student ... My favourite is Algebra and Calculus!!

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  19. The answer is no, any number in series can not be divisible by 7. 777 is.

    Secondly I think that Indian system of teaching mathematics is a lot teacher dependent, I have had some awesome math teachers.

    Thirdly, fun or not, but India System of teaching maths is effective. Ask all the US & UK ppl who keep struggling at elementary mathematics in GMAT and GREs of the world where Indian Student Rock the boat.
    I was talking to Japanese friend some days back, we were talking education and he said do they still make you learn tables till 20 * 20 and I when I said yes. He was Indian education is too good. It was a really proud feeling for me

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  20. British education rocks...and so does Math :O)
    My dad was a Mathe-magician :P ...mad about numbers, but for some reason those genes went to my brother.

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  21. Maths...nahii

    Preeti, I am going to run far far away if your going to post maths queries

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  22. 777 does nt give a reminder when divided by 7..778 does..So the seq should have 778

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  23. Here it goes...

    If a number is to be in that sequence.. that number minus 1 should be a multiple of 7 as listed below.
    1 - 0 = 7 x 0
    8 - 1 = 7 x 1
    15 - 1 = 7 x 2
    21 - 1 = 7 x 3
    ......

    But
    777 - 1 = 776 and not a multiple of seven.

    So, 777 is not in that sequence..

    Am I right?

    Cheers:-)

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  24. Repetition, I know...but still...

    Since we are starting with 1 and adding 7 to each number, the series goes like 1+7+7+7.

    Since multiplication is repeated addition, this means that each number in the series is 1 plus a multiple of 7.

    Or.. any number in the series minus 1 is a multiple of 7.

    So to find out if 777 is in the series, subtract 1 and see if it is divisible by 7.

    If I was a math teacher, though...I wouldn't explain any of this and would get them to arrive at the answer themselves by asking leading questions and making them work out the solution.

    As you can see we have had people explain the same thing in two different ways..i.e. talking about 777+1 and about 777-1. So each child should be able to work out his/her own solution/explanation. Or so I think! :)

    Interesting, PS!

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  25. Well, I would be pretty late in commenting about this, but just got hold of your book last week and read it in 2 go's !
    It is indeed a treasure these days to find people who have the ability to write about real life incidents with such humorous details. Not to forget, the wonderful gift of gab! Nice piece of work and its good to know that there are people who can share their experiences so well. It kind of helps someone else suffering through the same things to know that every phase does get over and one is eventually pulled out of it.
    Your first story gave me goosebumps and your resolutions made me ponder. This book definitely becomes a gift for all the candies of my life!

    Great work and continue your multi-tasking adventurous life !

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  26. Well, since lots of people have already given really good explanations, let me turn this over its head and give a problem :

    consider
    1 4 9 16 25 36 ..
    (squares)

    Will 678947956783 be on this list?

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  27. hmmmm....
    the outright explanation is this is a sequence which follows the rule of (1+7x). where x = 0 to infinity. Based on that it is easily discernible that 777 cannot be part of the series.
    Explanation:
    the 2nd term of the sequence is, t2 = 1+7*1 = 8
    similarly, t3 = 1+7*2 = 15
    therefore, t112 = 1+7*111 = 778
    hence proved.

    On a simpler note, if we discard the first number, and decide to subtract 1 from the rest of the numbers in the series then, they would be divisible by 7. (allow the child to test this theory)
    but, if 1 be taken from 777, then 776 is not divisible by 7. So, going by the rule that we had established for a number to be part of this sequence, can 777 be part of the sequence? (if thy be successful, the child shall answer NO. Should the answer be YES/I Don't know, repeat process!!).

    Note: If the child asks why divisible by 7, one has to explain that since the sequence is increasing by 7 for each term, thus if the starting number be taken off then all number should be divisible by 7 since repetitive addition is multiplication. (again its best to allow the child to test the theory, unless he/she is aware of it already)

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  28. Answer to the anonymous poster's question : No, because the sequence is of perfect squares (of natural numbers). And no perfect square can have 3 as the digit in the units' place.

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  29. @PS - Sorry for turning this sanctum sanctorum of literary expression and human emotions into a cold digital mathematical vector field :) But I used to love calculus, algebra, functions, coordinate geometry, matrices.... :)

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  30. i've noticed that posts with questions which challenge people always gets more responses than others... don't you agree? :)

    the answer has been given by almost everyone before this... and the most elegant explanation is that each number is 1 more than a number divisible by 7 and therefore 777 cannot be in the series since it is divisible by 7.

    i agree that subjects like maths and even civics can be made so much more fun!

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  31. ok, im late and everyone above me has already said the answer.. still, have to prove that the maths is studied was worth something..
    so ya, 777 cant come in there cos its divisible by 7 and those numbers in sequence are all one more than multiples of 7..tada !!!

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  32. P.S. will i be getting my "King of Maths 2009" award in the mail at Pune or Kannur :)

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  33. And the Fields Medal goes to??? :)

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  34. Lol! What a thing to make us reminisce school?! :)

    It's simple actually.

    1,8,15,22,29...

    Each of these numbers aren't divisible by 7, but 777 is and hence, it won't appear in this sequence.

    However, each of this number after 1 will be divisible by 7 if you take the next consequent number and minus 1 from it.

    Eg: 8-1 = 7 (Divisible by 7)
    15-1 = 14 (Divisible by 7)

    So on and so forth.

    Therefore, the number that will appear in this sequence will be 778.

    Why? Well, 778-1 = 777 (Divisible by 7)

    C'est tout!

    Thank you :p

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  35. Ohh noooo.. no math for me plsss :)

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  36. i HATE math!!
    loathe it.
    but the answer was pretty simple, no!

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  37. The series goes like..

    (0 x 7) + 1 = 1
    (1 x 7) + 1 = 8
    (2 x 7) + 1 = 15
    .
    .
    (11 x 7) + 1 = 78
    .
    .
    (111 x 7) + 1 = 778

    voila! just missed 777 by 1 run :D.. so the answer is NO..

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  38. I am not even attempting to answer since so many have already done it.
    Just wanted to share a link to some hilarious answers to maths tests. The last one is the best :-)

    http://cr4.globalspec.com/thread/7484/Funny-Math-Answers

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  39. I HATE math..with quite some passion.mabbe ‘coz I can never crack the problems. OR mabbe I can never crack the probs ‘coz I hate math !

    Anywez..giving this a shot ,knowing very well that I won’t be a contender for one of the 2 names…
    777 will not be part of the series ‘coz it is divisible by 7. If u notice, the series has numbers that are divisible by 7 +1 eg 8 , 15 (14+1), 22(21+1) and so on. Therefore 778 (777+1) will be part of series, not 777!

    I’m so anxious to know if my ans is right or wrong! Phew! I need a drink!
    ______________________

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  40. This post has been fun!!! I had a good time giving my grey matter something to work on. Besides, I've been reading up on farthingale, parlet and dumbroll...LOL. Though, I do think it has to be bumroll and not dumbroll:)

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  41. NO..777 wont be in the sequence as the seq contains 1 more than multiple of 7.

    But the machine was gr8 fun :)

    Sorry, as i was really busy yesterday and even today till now i could not update my blog..will do it for today though...

    have a nice day
    cheers,
    shantharam

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  42. I was good at Maths in school but growing up it got rusted.. :D

    The answer is already out so no point in posting it, though I am happy I got that right.

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  43. Nice one!! This post reminded me of my childhood when every uncle and aunt would cuddle me and ask
    "Beta! which subject you like the most?" and I used to reply "Maths" but honestly speaking I was more close to English..Anyway solving the sequence was fun...
    For the answer to blog post 8 I have to say that I am still in search of that elusive human being.

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  44. Good question - I'll admit I had to think little bit before getting it, and my explanation wud be the same as many above :)

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  45. @Anony: absolutely not (provided we are considering natural numbers only)!! as Ajay had pointed out...
    all natural number squares should end with either of the following digits - 0,1,4,9,6,5.

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  46. No, it will not be available.

    Explanation -
    Calvin:the sequence follows a pattern. What pattern is it?
    Hobbes: Hmmm...I do not know...wait a minute they mentioned 7...so is it multiples of 7 (for average Joe, or 7 tables for Janakiraman)
    Calvin: No, you muppet! There is no 7 in 7 tables...so it cannot be that. Ha! It is multiples of 7 + 1!
    Hobbes: Then, how will you get 1 in the beginning?
    Calvin: I will start with 7 multiplied by 0!
    Hobbes: So, as 777 is a multiple of 7 (like, 7 and 77), I know I will not get that in the sequence. QED!
    Calvin: I solved it...and you are claiming QED!
    the argument continues.

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  47. Bowing with humility :)
    Now raising both hands clasped together above my head and grinning at the crowd :)
    Now blowing kisses and waving to the crowd applauding me for the Fields Medal.
    Thanks Preeti :)

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  48. Good post.. interesting replies and awards :)

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  49. I'm so glad I've replied to this after the result has been given...my Math ability is second to none...but on the other side of none..ie: in minus figures...I'm rubbish!

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  50. Nice one Preeti
    Have you ever tried "Car Numberplate Game" for mathematics. I somehow love this game and is my favorite timepass on the drive.

    As rightly said, you can either love it or hate it. I used to hate it till the time i was studying, but somehow now I Love mathematics

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