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Math Quiz


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A problem was given to me by a 5th grade child
i found it very interesting so who ever solves it out first gets a WP

So here it is and good luck

A 4 digit number divided by its inverted self equlas 6 and rest 933

Find the number knowing that the difference between the first digit and the last equals 7 and the difference between the 2nd and 3rd digit equals 2.

There are 2 ways of solving this so there will be 2 WP as reward for those who give out the correct and full mathematical explanation.

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[quote name='Malaikat Maut' date='28 October 2009 - 08:45 PM' timestamp='1256762723' post='45980']
What do you mean it equals "6 and rest 933"?

The number doesn't divide perfectly ..it has a rest

P.s the deduction method was found by Shadow .

still waiting for the 2nd method

Edited by Indyra
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[quote name='Indyra' date='28 October 2009 - 09:12 PM' timestamp='1256760774' post='45975']
A 4 digit number divided by its inverted self equlas 6 and rest 933
I think you meant divided by it's mirror. The inverse of x is 1/x (in most contexts) and dividing x by it's inverse is equal to squaring x, which obviously wouldn't make sense in the context.

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After reading your answers i just figured the there is no 3rd way of solving this because the 2nd and 3rd methods are almost identically

So the quest has now ended : the winner are Shadow seeker and Kafuuka

The solutions were

Shadow Seeker

We know 6x+933=Y
And that if we write the number as WYXZ that W-Z=7
Since it is 6 times higher that the reverse, Z has to be 1 and W 8
Otherwise the equation would make no sense.
We're dealing with numbers out of N, so only these work, although theoretically 7 and 0 work as well. The issue with 6x (lower than 1k)+ lower than 1 k is that it won't reach 7 k, so we know it's 8 and 1, since 2 *6 isn't anywhere close to 9 and exceeding the limits.
The next step is the missing two numbers from the mid, all you need is just a little testing with the numbers you input 97, 86, etc and go down using a calculator: everything that divided by it's reverse gets 6 is marked and then you just check which is the right one.


and Kafuuka's
a * 1000 + b * 100 * c * 10 + d - 933 = 6* ( a + b *10 + c *100 + d *1000 )
|a - d|= 7
|b - c|= 2

994 a + 40 b - 590 c - 5999 d = 933

from this we can guess a should be larger then d, thus a = d + 7
trying b = c +2 or c - 2:

994 ( d +7) + 40 ( c +? 2) - 590 c - 5999 d = 933
- 5005 d - 550 c = - 6105 +160?
d = 1
c = 2

a = 8
b = 4

8421 - 933 / 1248 = 6

Edited by Indyra
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