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June 27th, 2016, 11:10 AM   #1
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Problem involving cubed numbers

ABCD - DCBA = A^3 + B^3 + C^3 + D^3
ABCD and DCBA are four digit numbers.
A, B, C, D are different numbers between 0 and 9.
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June 28th, 2016, 04:50 AM   #2
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You really did not ask a question. Do you want the answer (which we tend not to give for homework) or help finding the answer.

If the latter, this kind of problem teaches you how to use information that is general knowledge but not explicit in the statement of the problem or that is implied but not obvious from the problem itself.

Where I would start is with this: a, b, c, and d are non-negative. And we are dealing with FOUR digit numbers. So a and d are greater than 0. Do you see why?

So $a^3 + b^3 + c^3 + d^3 > 0 \implies d \not > a.$ Why?

But the problem says a and d are not equal so $1 \le d < a \le 9.$

What thoughts do you have about what to try next?
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June 28th, 2016, 06:13 AM   #3
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Here's another hint for problems like this:

if ABCD is a four-digit number where the digits have been replaced with letters, then an equivalent description of the number is

$\displaystyle 1000A + 100B + 10C + D$

where A, B, C and D are now algebraic variables (and also integers).
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June 28th, 2016, 11:24 AM   #4
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Quote:
Originally Posted by JeffM1 View Post

And we are dealing with FOUR digit numbers. $\displaystyle \ \ \ \ $ This means there are four numbers,
which is not what you intended.

No, we are dealing with the difference of two four-digit numbers. Do you see the importance of the hyphen?


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As another true example, there was a sign on a wall in a Kroger supermarket deli that read: "No sugar cookies are here!"

I asked a worker, "When will the sugar cookies be here?"

The hyphen makes all the difference.
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June 28th, 2016, 12:42 PM   #5
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Quote:
Originally Posted by Math Message Board tutor View Post
No, we are dealing with the difference of two four-digit numbers. Do you see the importance of the hyphen?


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As another true example, there was a sign on a wall in a Kroger supermarket deli that read: "No sugar cookies are here!"

I asked a worker, "When will the sugar cookies be here?"

The hyphen makes all the difference.
I presume that someone who asks this sort of a question is not an idiot.
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June 28th, 2016, 07:56 PM   #6
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Quote:
Originally Posted by JeffM1 View Post
I presume that someone who asks this sort of a question is not an idiot.
No, instead of making that reply, you would type something back to me along the lines of,
"Thank you for correcting me. I hadn't noticed what I typed didn't make sense."
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June 29th, 2016, 01:23 AM   #7
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Quote:
Originally Posted by Math Message Board tutor View Post
No, instead of making that reply, you would type something back to me along the lines of,
"Thank you for correcting me. I hadn't noticed what I typed didn't make sense."
MMBt... perhaps you should have a think about what it was about your message that yielded the response you didn't anticipate rather than just demand what responses you want from people.

Hint... look up the meaning of the word "pedantry"
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