Norman Silverstone <[EMAIL PROTECTED]> wrote: ... > challenging. What I am thinking about at the moment is how to program for > the computer to guess the number which I select. I know it can be done but > I suspect it requires an approach which I have not yet learnt. I would > welcome suggestions on the best way to approach this problem.
I assume the way the computer is going to guess is by trying some number, and you respond either that it's guessed right, or to go lower, or to go higher. In that case, think of "bisection". Originally, all the computer knows is that the number is in some range, say 0 to 100. It can then guess the midpoint, 50. If it's right, yay! Otherwise: if it's told to go lower, then the range is now 0 to 49 -- if higher, it's 51 to 100; in each case the range was just halved (actually, a bit more than halved). It does not take many halvings to squeeze even a pretty large original range down to a range which only includes one possible number... that's because "2 to the power of N" grows VERY fast with N, as the old story about the inventor of chess shows (the king told him to ask for a reward, and all he wanted was some rice -- one grain on the first cell of the chessboard, two on the next, then four, eight... all the way through the 64 squares of the board; the kind thought the inventor was being very moderate in his request, and granted it... to soon find out that not enough rice existed in the world to satisfy the request...;-). Well, repeated halving is just like repeated doubling "backwards", so it squeezes vast ranges of possibilities down to tiny ones just as fast as repeated doubling produces oceans of rice from a small chessboard;-). Alex -- http://mail.python.org/mailman/listinfo/python-list
