SOLUTION: Hi, abc + de be =bdc, what is the solution

Question 1209560: Hi,
abc
+ de
be
=bdc, what is the solution
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I will assume the cryptarithm is this:


  ABC
   DE
 + BE
  ---
  BDC

This is not a very well-made cryptarithm; there are many solutions.

(1) In the units column, C+E+E yields final digit C. That means E is either 0 or 5.

(2) In the tens column, B+D+B, plus possibly a carry of 1, yields digit D in the sum, so B is also either 0 or 5.

(3) Since in the tens column B+D+B yields digit D in the sum, there can not be a carry of 1 from the units column.

(4) From (1), (2), and (3), E must be 0 and B must be 5.

(5) In the hundreds column, A plus a carry of 1 yields leading digit B (=5) in the sum, so A is 4.

So we know the addition looks like this:


  45C
   D0
 + 50
  ---
  5DC

There are no further restrictions, so C and D can be any digits. The three digits 0, 4, and 5 have been used; assuming the letters represent different digits, there are 7 choices remaining for C and then 6 choices remaining for D, making a total of 7*6 = 42 solutions.

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