You can see in Figure
1 this average result A1
as a function of the answer y.
We get the maximum result by solving dA1/dy = (-2y+193)/198 = 0 which corresponds to y=193/2=96.5 : the most near integer values y=96 and y=97 have the same average result of 49.080808 |
![]() Figure 1
Average results face up equiprobabilistic answers |
I've implemented this iteration in language C (you can get the source code in http://www.uv.es/pla/models/viajero/viajero.c) and got the successive maximum average results from integer answers, which are: n= 1: A(96)=49.080807 A(97)=49.080807 n= 2: A(96)=59.993732 n= 3: A(96)=60.926846 n= 4: A(96)=61.021133 n= 5: A(96)=61.031261 n= 6: A(96)=61.032364 n= 7: A(96)=61.032497 n= 8: A(96)=61.032520 n= 9: A(96)=61.032509 n=10: A(96)=61.032516 n=11: A(96)=61.032509 n=12: A(96)=61.032513 n=13: A(96)=61.032524 n=14: A(96)=61.032513 n=15: A(96)=61.032524 (from n=13 the results happen again cyclically) |
![]() Figure 2
Average results in the first step (green) and in the 30th step (blue) |