Given the sums below, where the digits were replaced by letters (same digit, same letter; different digits, different letters):
A B C D A C F F A A D B
+ E E F F + F F F + A A A
------- ------- -------
F C C E B C F B B D C DIdentify the value correspondent to each letter.
Well, we're not in base 10. I'll let you figure out why that is the case (besides the title, which is a hint).
Let's solve assuming Base X, which is unknown.
From addition 2:
a) F + F = B + X (because it must carry to next column)
F + F + 1 = F + X (because it must carry to next column)
solves to F = X - 1
B = X - 2
b) A = B - 1 = X - 3
From addition 3
c) B + A = D + X (because it must carry to next column),
so D = X - 5
d) 1 + D + A = C + X (because it must carry to next column),
so C = X - 7.
From addition 1
e) D + F = E + X (because it must carry to next column),
so E = X - 6
f) 1 + A + E = F (because it carries from previous column)
1 + (X - 3) + (X - 6) = (X - 1),
so X = 7. We are in Base 7!!!
Than ABCDEF = 450216
Additions (Base 7) are
4502 4066 4425
+ 1166 + 666 + 444
------ ------- --------
6001 5065 5202
Edited on June 25, 2008, 1:19 pm
Edited on June 25, 2008, 11:39 pm
Not In Kansas Anymore (spoiler)
