Sign up ×  Some ETs follow a positional number system, with the
same base as the number of fingers on their hand. The following
inscription is all the evidence we have: $$(\Box @)+(\Box @) =
\Box\bigstar\Box $$ Find the number of fingers.  Attempt:
$(xy)_b + (xy)_b = (xzx)_b$ Can be written as $2y+2bx=x+bz+b^2
x$ so I need to solve for $b$ the equation $b^2x+bz-2bx+x-y=0$
with $b\geq 2$ and $0\leq x,y,z<b $.  share|cite|improve this
question Regarding Source, M Gardner's mathematical games was
mentioned in the book, but I havent been able to locate it.
Please post an online link if you know it. –  kuch nahi Jun 26
'11 at 9:41 my interpretation of $(\Box @)+(\Box @) =
(\Box\bigstar\Box)$ is $(xy)_b+(xy)_b=(xzx)_b$ and therefore
$(bx+y)+(bx+y)=b^2x+zb+x$, which can be transformed into
$2y+2xb=(b^2+1)x+bz$ –  miracle173 Jun 26 '11 at 9:42 Hint: When
adding two double 'digit' integers together, the maximum carry
you can get to the third position is equal to ... –  Jyrki
Lahtonen Jun 26 '11 at 9:43 @miracle173 mad