Please answer the question completely; Use strong induction to show that the ali
ID: 2261242 • Letter: P
Question
Please answer the question completely; Use strong induction to show that the alien merchants are right and then argue why they can't pay for an article worth 23 dollars.
(Currency in alien society.) Suppose we are in an alien society which through tradition places a special importance on the twin primes 5 and 7. For this reason, they make only two type of coins one worth 5 dollars and the other worth 7 dollars. Through trial and error merchants think that you can sell items at any price that is at least 24 dollars using a combination of 5 and 7 dollar coins, we are able to create any quantity of money worth 24 dollars or more. For instance since 24 = 2(5) + 2(7), we just need two 5-dollar coins and two 7-dollar coins to pay an article worth 24 dollars. Use strong induction to show that the alien merchants are right. Then argue why they can't pay for an article worth 23 dollars. (Make sure to include all the needed cases in the base case).
Please answer the question completely; Use strong induction to show that the alien merchants are right and then argue why they can't pay for an article worth 23 dollars.
Explanation / Answer
To purchanse any article we need to use only $5 & $7.
However we can't acieve $23 in anyway!
If we use, one coin only - $5 & $7
If we use, two coins - $10, $12 or & $14
If we use, 3 coins - $15, $17, $19 & $21
If we use, 4 coins - $20, $22, $24 & $28
but we can't aciever $23.
Even if we use, 5 coins we will achieve minimum of $25 only, hence $23 is impossiple to achieve.
That's why all the alien merchants are right. They Can't pay for an article worth 23 dollars.