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I need help knowing how numbers can be in place of these letter twice...
Numbers being down as 285714 and 142857
There are two different ways to solve it and does A get counted as 1 or 0?
i'm lost
please help!!!
ABCDEF × 3 = BCDEFA
The Solution . . .
285714 × 3=857142
or
142857 × 3=428571
Last edited by XxMathCuriousXx (2009-02-05 14:25:13)
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Like why those numbers like how you get it... I thought again A is 0 or 1...
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Since they're arranged in the same order both times, you can think of BCDEF as a single variable.
So now you have AZ x 3 = ZA
Translating this to a 'standard' equation:
(100000A + Z) x 3 = 10Z + A
Rearrange for Z:
300000A + 3Z = 10Z +A
299999A = 7Z
Z = (299999/7)A = 42857A
Now, A is a single-digit number, so that means there are only a few possibilities that could work.
A=1 --> Z = 42857, which gives 142857 as a solution.
A=2 --> Z = 85714, which gives 285714
A=3 --> Z = 128571. However, Z is a 5-digit number, so this is too high.
The same goes for any value of A higher than this.
(Technically, you could also put A=0 --> Z=0, giving 000000 as a working answer. Not sure if you want to allow that)
Why did the vector cross the road?
It wanted to be normal.
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