# Digits

Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.

Result

a =  198

#### Solution:

$a=zyx-xyz \ \\ a=100 \cdot \ (x+2) + 10(x+1) + x - (x \cdot \ 100+(x+1) \cdot \ 10+(x+2)) \ \\ a=100x+200+10x+10+x-100x-10x-10-x-2 \ \\ a=200 + 10 -10-2=198$

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