Chris Angelico asked: what does a negative string look like? This is a very good question. It looks a bit like a negative number. >>> 2 + 2 4 >>> len('aa' + 'bb') 4 >>> len(-'bb') -2 # Odd, I must confess. >>> 5 + (-1) 4 >>> len('hello') 5 >>> len(-'o') -1 >>> 'hello' + (-'o') 'hell' >>> len('hello' + (-'o')) 4 Grade school: How can I possible have -3 apples in my bag. University: How can I possibly be overdrawn in my bank account. Negative strings are similar to negative numbers except: For numbers a + b == b + a For strings a + b != b + a It is the non-commuting that make negative strings difficult. This is a bit like computer programming. It's not enough to have the correct lines of code (or notes). They also have to be put in the right order. I hope this helps. I do this sort of math all the time, and enjoy it. Your experience may be different. -- Jonathan