Posted by lori on Sunday, November 4, 2012 at 1:49pm.
Use trial and error.
The hundreds digit is 6, 7, 8, or 9
The ones digit is 0, 1, 2, or 3
The tens digit is 7, 8, or 9
Can you figure this out now?
if hundreds-ones=6, then we have
9x3
8x2
7x1
6x0
Since the digits add to 19, 7x1 and 6x0 are out, leaving
9x3 or 8x2
If tens is greatest, 9x3 is out, so we must have
892
This must be the number, since the only other choice would be 298, where the difference between hundreds and ones is still 6, but in the other direction
x y z
x + y + z = 19
|x-z| = 6
x >/= 5
y >/= 6
so x+y >/= 11
so z </= 8 to get 19 sum
z < 6 because y is biggest
choices
x 5 6 7 8 9
y 6 7 8 9
z 0 1 2 3 4 5 6 7 8
but x and z differ by 6 so
x 5 6 7 8 9
y 6 7 8 9
z 0 1 2 3
now what adds to 19 there with y biggest?
none until y = 9
so x 9 z
but x and z differ by six
8 and 2 differ by six
8 9 2 ?
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