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WHY is it always 1089? anyone can explain?

the answer is always 1089 when you do this: choose whatever 3numerals containing number from 1 to 9 ... e.g. : 426 ok?
and now... write this number from backwards.. you will get 624, right? and now subtract these two nubers: 624-426.. you will get another number: 198 .. do the same with this one: write it backwards and subtle these two: 891-198... you will get 693.. and now write it backwards and ADD these two numbers... : 396 + 693.. and you will get 1089 !!! I tried it with another numbers.. it is the FACT !!! always 1089.. WHYYYYY???
I got this task from my boyfriend.. he still hasnt explained me why it is like that :p )
Posted 4 months ago
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I don't have the solution, but I can point out a couple of interesting features that may shed a little light.

(1) In almost all cases, you don't need three steps, you only need two. Once you select your first number and do the first subtraction, no matter the number, you will wind up with either 693 or 198. Either of these will get you to 1089. You don't need that third step.

(2) Except that you do need the third step when, as koyptakh points out, there is not a sufficient difference between digits. Meaning, basically, 6 and 5. For example, 625-526=99. In that case you need a third step. 990-099=891 (which is the reverse of 198, and therefore gets you to 1089).

(3) 9 is the magic digit here. 1089, 693, and 198 are all divisible by 9. 9 does similar magic things elsewhere: try that first step with a two-digit number instead of three. When you do the subtraction, you will always get some multiple of 9. Perhaps because there are 9 digits total, not counting zero. Perhaps because 9 is just the square of 3, which is a simple number to manipulate.

Somehow, when you do that step with a hundreds-place digit -- that is, you are using 3 unique digits -- it drastically narrows the possible result when you do the subtraction. From there, it's a quick jump to 1089.
Posted 4 months ago

Other 6 Answers to WHY is it always 1089? anyone can explain?


Posted Jul 5th, 2009 at 8:15AM
Well, what I figured out is this:
when you subtract the number you chose with its reverse, the middle number will stay constant, lets solve 842-248, you have to take 1 from the second no. so you can subtract 2-8 so it will be 12-8=4 and then the second no. 4 will be 3 which which will bcome 13-4=9, the answer will always be 9. So 842-248=594, notice also that the 1st no. 5, if you add it with the 3rd no. 4, you will also get a 9. why is this necessary to tell you? bec. of this: It's always reversing the 1st and the 3rd no. right? so adding the 1st with 1st will have the same result as adding with 3rd and 3rd (like 594+495 (5+4=9 and 4+5=9)
That's why you get 1089 everytime, bec. the 4th no. 9 is a result of the 4+5. The 3rd no.8 is a result of the constant 9 (9+9=18 and you only put the 8 and move the 1 to the next number))you get 10 (1089) from 4+5 bec. when you add the 9+9 it will result in 18, you'll put the 8 down and move the 1 to the next add (4+5) and you'll have to add a 1 with them so you get 10
and there you have it, you will always get 10 8 9

Ofcourse under two conditions, which were stated above

I don’t know if anyone will understand what I wrote,I think it is poorly written lol, but I don't care, I'm glad I figured it out.
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Posted Jul 4th, 2009 at 2:41PM
We'll I just learned something new today:)
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Posted Jul 4th, 2009 at 2:47PM
What about 111, 222, 333, ect? :P
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Posted Jul 4th, 2009 at 2:47PM
You do realize that last night MANY people partied and are hung over today. Or are partying today and will be hung over tomorrow..anyway that question made my head hurt and although I drank last night..my brain is clear. I imagine other's brains are near the breaking point! But all the same..I second laceset.
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Posted Jul 4th, 2009 at 2:52PM
No, I can't explain it. I'm a social scientist, not a mathematician. I don't care about numbers except where my checkbook is concerned.
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Posted Jul 4th, 2009 at 2:53PM
Hi bublina
You are right.
Take any 3-digit number in which the first and last digits differ by 2 or more. Reverse the number, and subtract the smaller of the two numbers from the larger (e.g. 782-287=495). Then reverse the result and add (thus 495+594=1089). The remarkable thing with this is: the result is always 1089, no matter which 3-figure number you start with.

Mathematics is an art creating poetry with numbers as if with letters and words.
:)
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