
The only screens that are significant are the two with all the numbers. In the first screen all the numbers are divided into five colours. You pick one and state the colour - thus narrowing things down to one of five possibilities. When you get to the screen with the houses with all the numbers is, there is one number of each of the original colours in each of the five houses. Therefore by picking your number on this screen, you are telling the program which is your number. You can lie to the other screens because the computer only needs those two to work out which is your number.