Am I understanding this question correctly and how do I approach these problems?
In Numberland, the unit of currency is the El (E). The value of each Numberlandian coin is a prime number of Els. So the coin with the smallest value is worth 2E. There are coins of every prime value less than 50. All payments in Numberland an exact number of Els.
(a) What is the smallest payment (without change) which requires at least 3 coins?
My opinion: This seems a bit too obvious which is why I am uncertain. If the smallest is 2E then then the smallest payment that requires 3 coins would be 6E. Is this question actually this easy or am I misunderstanding it?
(b) A bag contains 6 different coins. Alice, Bob and Carol take 2 coins each from the bag and keep them. They find that they have all taken the same amount of money. What is the smallest amount of money that could be in the bag? Explain your reasoning.
My Opinion: I am still unsure of how to approach this question. Help would be appreciated.
(c) Find 5 Numberlandian coins which, when placed in ascending order, form sequence with equal gaps of 6E between their values.
My Opinion: Assuming that I am not misunderstanding the question I got 5, 11, 17, 23, 29 simply by writing down the first few primes and looking for this pattern.
(d) The new leader of Numberland decides to mint coins of prime values greater than 50E. Show that no matter what coins are made, there is only one set of 5 Numberlandian coins which, when placed in ascending order, form a sequence with equal gaps of 6E between their values.
My Opinion: Still Unsure of how to approach it. Help would be appreciated.
Please check my answers and advise on how to solve the questions I couldn't solve.
Thank you so much :)