Induction extravaganza

Prove, for all n, an + bn <= (a+b)n

Can do this proof directly or indirectly.

Prove you can make any value of postage (more than 8 cents) just from 3 and 5 cent stamps.

Soft introduction to what the book calls "strong induction".

Tower of Hanoi. Prove (inductively) that you can solve the tower of hanoi problem for any number of disks.

NIM. Two piles. either player can take as much or as little from one pile (must take something). last person to take something wins.

Prove, if A = B and it is player one's turn, then player 2 can force a win.