4.4.1

4.4.5 Problems P4.4.1 Consider a variant of Exercise 4.4.3, for $4 and $11 bills (made, we might suppose, by a particularly inept counterfeiter). What is the minimum number k such that you can make up Sn for all n 2 k? Prove that you can do so. P4.4.2 Give a rigorous proof, using strong induction, that every positive natural has at least one 4.4.5 Problems P4.4.1 Consider a variant of Exercise 4.4.3, for $4 and $11 bills (made, we might suppose, by a particularly inept counterfeiter). What is the minimum number k such that you can make up Sn for all n 2 k? Prove that you can do so. P4.4.2 Give a rigorous proof, using strong induction, that every positive natural has at least one