[MOVED] Fill in the letters using numbers 1-9

[khkamxb]

In the addition problem below, each letter represents the same digit in both problems. Relace each letter with a different digit, 1 through 9, so that both addition problems are true. (there are two solutions)

  ABC    ADG
+ DEF  + BEH
-----  -----
  GHI    CFI

We were given A = 1 and H = 2.

Been working on it for hours and haven't gotten anywhere but stress out..hope soeone out there can help! Thanks

 

[stapel]

There is, to my knowledge, no "formula" for this sort of arithmetic puzzle. You just have to try the various options, and see what works.

For a start, you know that you cannot have a sum of 10 or greater in the hundreds column of either addition, since neither addition has a "carry" into the thousands column of the answer. This can limit the values of the hundreds, and possibly the tens, columns.

You say you are given two of the values, so you actually have:

  1BC    1DG
+ DEF  + BE2
-----  -----
  G2I    CFI

This means that you have the following additions:

. . . . .B + E = 2 (or B + E + 1 = 2, if there's a "carry")

. . . . .G + 2 = I (or G + 2 = I + 10, if there's a "carry")

So start guessing values for G, B, and E, and see where things lead.

Eliz.