Claim. The Inductions can make change for any amount of at least 85g where Sg (Strongs) represents the currency units for the country Inductia. Also, the country only has 38g and 55g coins. The following sentences are enumerated. Put them in order as presented in the lesson material to create a proof of the Claim that uses an induction argument. Enter your answer as a 17 digit integer. (For example, 12345678910111213 is in a valid format for an answer, but it is incorrect.) 1. 2. That is, they can make change for any number of eight or more Strong. We prove by strong induction that the Inductians can make change for any amount of at least 85g. . The induction hypothesis P(n) will be: There is a collection of coins whose value is n + 8 Strongs. Base case: P(O) is true because a 35g coin together with a 55g coin makes 85g. We argue by cases: Now by adding a 35g coin, they can make change for (n + 1) + 85g, so P(n + 1) holds in this case. We now proceed with the induction proof: Inductive step: We assume P(k) holds for all k S n, and prove that P(n + 1) holds. Case (n + 1 2 3 ): Then 0 g n 2 g n , so by the strong induction hypothesis, the Inductians can make change for (n 2) + 85g. Since P(n + 1) is true in every case, we can conclude by strong induction that for all n 2 0 , the Inductians can make change for n + 8 strong. . Case (n + 1 = 1 ): We have to make (n + 1) + 8 = 9Sg. We can do this using three 35g coins. Since n 2 0 , we know that n + 1 2 1 and thus that the three cases cover every possibility. _ . Case (n + 1 = 2 ): We have to make (n + 1) + 8 = 105g. We can do this using two 55g coins