Using only the digits 0-9, but not 3 or 5, solve for each letter:

GRAPE - PLUM = APPLE

You can only use one digit for each letter.

I've found a solution, but haven't worked through the other options to see if it's unique...

GRAPE = 94872
PLUM = 7160
APPLE = 87712

Some workings to get there...

Firstly, M must be zero since E-M=E.
Secondly, G=A+1 since GRAPE is a 5 digit number and PLUM is only a 4 digit number.
Thirdly, P>R since G can't equal A.

Assuming P>U then P-U=L (from the 10s column)
Assuming A>L then A-L=P (from the 100s column) - this gives A>P

These equations show that 2P=A+U

Since P>R then R+10-P=P (from the 1000s column)
So P=5+R/2 which gives either (R=2, P=6) or (R=4, P=7) - P can't equal 8 or 9 since G>A>P

Using P=6 in the 2P=A+U equation gives R=L=2 which is invalid

Using P=7 in the 2P=A+U equation gives the above answer.

There may be alternative solutions if you assume U>P...

Posted by fwaff on 2003-02-17 07:11:57