Huiliang received $150 in simple interest one year from three investments. Part is invested at 1.5%, part at 2%, and part at 3%. The amount invested at 2% is twice the amount invested at 1.5%. There is $400 more invested at 3% than at 2%. Find the amount invested at each rate.

(a) What is the least number of moves needed to move 3 disks? 4 disks? 2 disks? 1 disk?

(b) Conjecture a formula for the least number of moves needed to move n disks. Prove it by mathematical induction.