english: For the 5-coin problem the solutions are (5,15,25,30,65), (5,15,35,45,50) and (5,20,30,45,55), each of which requires an average of 1.84 coins per transaction, and for the 6-coin problem the solutions are (5,10,25,40,45,50), (5,15,20,25,40,70), (5,15,20,40,45,55), (5,15,20,45,55,80), (5,15,25,30,60,65), (5,15,25,30,65,70) and (5,15,25,35,45,50), each of which requires an average of 1.68 coins per transaction.
non_english: BAA-KE5A BAA-KE5B BAA-KE5C BAA-KE5D BAA-KE5E BAA-KE5F BAA-KE5G BAA-KE5H BAA-KE5I BAA-KE5J BAA-KE5K BAA-KE5L BAA-KE5M BAA-KE5N BAA-KE5O BAA-KE5P BAA-KE5Q BAA-KE5R BAA-KE5S BAA-KE5T BAA-KE5U BAA-KE5V BAA-KE5W BAA-KE5X BAA-KE5Y BAA-KE5Z BAA-KE50 BAA-KE51 BAA-KE52 BAA-KE53 BAA-KE54 BAA-KE55 BAA-KE56 BAA-KE57 BAA-KE58 BAA-KE59