You can move from 1 to 2, 2 to 3, and so on, step by step, till 100. Also, between the points give below, you can move directly within every pair:
(10 and 60)
(50 and 100)
(70 and 100)
(80 and 100)
How many different paths exist? I tried it, and could find only 7. But a c-program i created says 8 paths. so, what do you think?
Here are the 7 paths in could find:
1-2-3....99-100;
1-2-3....10-60-61-62....100;
1-2-3....50-100;
1-2-3....10-60-61-62....70-100;
1-2-3....10-60-61-62....80-100;
1-2-3....70-100;
1-2-3....80-100;
It seems likely the "missing" path steps from 1 to 10, jumps to 60, steps backward to 50 and jumps from there to 100.
This shows a concise set of rules for allowable paths is important, since one interpretation would disallow going backward by steps from 60 to 50.