by Andrew_S » Sun 04 Nov 2007, 18:22:56
$this->bbcode_second_pass_quote('dinopello', '')$this->bbcode_second_pass_quote('SteinarN', 'I')'m pretty sure the right answer is 1001. I havent found a formula to get the answer, but i made a table. In the right upper corner there is only one alternative route, hence the numper one. In the field to the left from the right upper corner you have to go down to field 4 to have another path. From there it is 4 different paths to the lover left. In the field one mor to the left there is 20 different paths to the end. And so forth.
286+220+165+120+84+56+35+20+10+4+1=1001
_____________________________________________________
I1001_I_____I_____I_____I____I____I____I____I____I____I__1_I
I_286_I_220_I_165_I_120_I_84_I_56_I_35_I_20_I_10_I__4_I____I
I__66_I__55_I__45_I__36_I_28_I_21_I_15_I_10_I__6_I__3_I____I
I__11_I__10_I___9_I___8_I__7_I__6_I__5_I__4_I__3_I__2_I____I
I___1_I___1_I___1_I___1_I__1_I__1_I__1_I__1_I__1_I__1_I____I
Exactly.
*____1____1____1____1____1____1____1____1____1____1
1____2____3____4____5____6____7____8____9____10___11
1____3____6____10___15___21___28___36___45___55___66
1____4____10___20___35___56___84___120__165__220__286
1____5____15___35___70___126__210__330__495__715__1001
Although I did the table differently. The number of paths at any square is the sum of the number of ways to get to the one above and to the left.
Both are very nice. I like the simplicity of the last one.