2014 AMC 12B Problems/Problem 8
Revision as of 18:33, 20 February 2014 by Kevin38017 (talk | contribs) (Created page with "==Problem== In the addition shown below <math> A </math>, <math> B </math>, <math> C </math>, and <math> D </math> are distinct digits. How many different values are possible fo...")
Problem
In the addition shown below ,
,
, and
are distinct digits. How many different values are possible for
?
Solution
From the first column, we see because it yields a single digit answer. From the fourth column, we see that
equals
and therefore
. We know that
. Therefore, the number of values
can take is equal to the number of possible sums less than
that can be formed by adding two distinct natural numbers. Letting
, and letting
, we have
(Solution by kevin38017)