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Thread: Help w/ quiz: "You have six numbers: 123456. Divide 3-digit no. by 2-digit to get..."

  1. #1

    Help w/ quiz: "You have six numbers: 123456. Divide 3-digit no. by 2-digit to get..."

    Can you help with this?

    My 9 year old son was doing an online maghs quiz and asked for help, this was the question.

    You have six numbers: 123456
    Divide a three digit number by a two digit number to give a one digit number answer.

    I could not see anything like a logical way to tackle this? Something that he could do in his head, so, I asked him to figure out different ways to solve the problem.

    He thought that multiplying the two digit number by the one digit number would be a good way to go and set about doing it that way with a pencil and piece of paper. He very quickly realised that any answer containing a zero, a number above six, or a duplicate of the numbers he was using in his multiplication was incorrect, so went on to the next try. I did not time it but would guess he got the answer in under a minute.

    My question is: -
    Is there a more logical way of solving this problem?

    Thanks for any help..

  2. #2
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    It's not clear to me what is wanted. You say there are six numbers, then you speak of "0" and "above 6", which are not in the set of numbers you have. Are duplicates allowed?

    Trying to make sense of it, it may be that your three numbers need to come from the given six values.

    123 / 45 = 6 -- Nope
    452 / 61 = 3 -- Nope

    Just guessing. The hunt is still on.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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    Quote Originally Posted by Allan-k View Post
    You have six numbers: 123456
    Divide a three digit number by a two digit number to give a one digit number answer.

    I could not see anything like a logical way to tackle this? Something that he could do in his head, so, I asked him to figure out different ways to solve the problem.

    He thought that multiplying the two digit number by the one digit number would be a good way to go and set about doing it that way with a pencil and piece of paper. He very quickly realised that any answer containing a zero, a number above six, or a duplicate of the numbers he was using in his multiplication was incorrect, so went on to the next try. I did not time it but would guess he got the answer in under a minute.

    My question is: -
    Is there a more logical way of solving this problem?
    It sounds to me like he did EXACTLY what I would do. Good work! This IS logic, and very good logic at that.

    He used logic perfectly. First, he reversed the problem into a multiplication, which is much easier than division. Then, as I understand it, he probably looked at the single digit and the unit of the two-digit number and realized that he had to choose numbers that would give only digits 1 to 6 (and not a duplicate of the digits he was using), which greatly cuts down the number of tries needed. Precisely my own thinking.

    I can think of no "more logical way" to do it.

    Let's see ... those two digits have to be one of 2*3, 3*4, ... that's all they can be. And the tens digit has to be big enough to get a "carry" into the hundreds. So I try 2*43=86, 2*53=106, 2*63=126, 3*54=162 -- I've got it!

    Does that look something like what your son did? You can be proud.

  4. #4
    Quote Originally Posted by Dr.Peterson View Post
    It sounds to me like he did EXACTLY what I would do. Good work! This IS logic, and very good logic at that.

    He used logic perfectly. First, he reversed the problem into a multiplication, which is much easier than division. Then, as I understand it, he probably looked at the single digit and the unit of the two-digit number and realized that he had to choose numbers that would give only digits 1 to 6 (and not a duplicate of the digits he was using), which greatly cuts down the number of tries needed. Precisely my own thinking.

    I can think of no "more logical way" to do it.

    Let's see ... those two digits have to be one of 2*3, 3*4, ... that's all they can be. And the tens digit has to be big enough to get a "carry" into the hundreds. So I try 2*43=86, 2*53=106, 2*63=126, 3*54=162 -- I've got it!

    Does that look something like what your son did? You can be proud.
    Yes that does look similar to what he did, I'll try to attach his calculation paper... I can't?

    Anyway, thanks for the reply, I am proud of him and he does seem to like maths, let's hope that continues..

  5. #5
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by tkhunny View Post
    It's not clear to me what is wanted. You say there are six numbers, then you speak of "0" and "above 6", which are not in the set of numbers you have.
    They spoke of zero and digits greater than six as identifiers for results that need to be ignored.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    Quote Originally Posted by Allan-k View Post
    Yes that does look similar to what he did, I'll try to attach his calculation paper... I can't?

    Anyway, thanks for the reply, I am proud of him and he does seem to like maths, let's hope that continues..
    You should be able to attach a picture; if you have trouble doing that, let us know specifically what goes wrong (including if you just don't see the button labeled "insert image").

    Of course, you don't have to do it, but I'd be interested to see it. (Note that my explaining it probably took longer than it would have to think without writing, and that his writing probably doesn't make everything clear, since it wasn't intended as a communication! But we can make deductions; and if he wanted to explain what he did, it might actually be good for him -- it's called "metacognition", thinking about how we think, and can help us think better.)

  7. #7
    Quote Originally Posted by Dr.Peterson View Post
    You should be able to attach a picture; if you have trouble doing that, let us know specifically what goes wrong (including if you just don't see the button labeled "insert image").

    Of course, you don't have to do it, but I'd be interested to see it. (Note that my explaining it probably took longer than it would have to think without writing, and that his writing probably doesn't make everything clear, since it wasn't intended as a communication! But we can make deductions; and if he wanted to explain what he did, it might actually be good for him -- it's called "metacognition", thinking about how we think, and can help us think better.)
    I can't attach the picture, I think that it 'probably' exceeds the file size limit.

    As a jpg file it's 2.7MB as a pdf it's 162KB. Trying to upload it as jpeg, I just get an error message saying that it has not uploaded, doing the same with a pdf, it tells me that the file exceeds the limit of 19.5KB for this file type. That's what I've discovered so far..

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    Trouble uploading a picture

    Quote Originally Posted by Allan-k View Post
    I can't attach the picture, I think that it 'probably' exceeds the file size limit.

    As a jpg file it's 2.7MB as a pdf it's 162KB. Trying to upload it as jpeg, I just get an error message saying that it has not uploaded, doing the same with a pdf, it tells me that the file exceeds the limit of 19.5KB for this file type. That's what I've discovered so far..
    I'm new to the site and don't have a lot of experience with its limitations; but one possibility is to upload the picture to some picture sharing site and use Insert Image, From URL, turning off "Retrieve remote file and reference locally" (using the URL of the picture itself, not the page it is on). See the comments in the Read Before Posting message about not posting links to other sites, which is where I got this idea.

    Otherwise, you might need to use whatever software you might have for editing the picture, and reduce the file size (without making it unreadable). And that may be impossible.

    I'll hope someone with more experience adds other ideas.

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    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Allan-k View Post
    I can't attach the picture

    As a jpg file it's 2.7MB
    If you're using Windows, the snipping tool will capture select areas of your display -- creating JPG files with lower resolution (i.e., much smaller file size). Plus, it's a convenient way to crop off unnecessary stuff in margins while creating the image file itself. Generally, it's better to upload two smaller images than a single, large image.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  10. #10
    Quote Originally Posted by mmm4444bot View Post
    If you're using Windows, the snipping tool will capture select areas of your display -- creating JPG files with lower resolution (i.e., much smaller file size). Plus, it's a convenient way to crop off unnecessary stuff in margins while creating the image file itself. Generally, it's better to upload two smaller images than a single, large image.
    Thanks for the reply, yes, I'm using windows, will try chopping it down when I get back after the Christmas break.

    In the meantine, Merry Christmas and Happy New Year.. thanks for all the replies..

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