Question 84
A grasshopper starts at $(1,1)$ in the coordinate plane. It may jump between positive integral points $A,B$ exactly when triangle $OAB$ has area $1/2$.
1/ Determine all reachable points $(m,n)$.
2/ Prove that each reachable point can be reached in at most $|m-n|$ jumps.
1/ Determine all reachable points $(m,n)$.
2/ Prove that each reachable point can be reached in at most $|m-n|$ jumps.