part2 (2635B)
1--- Part Two --- 2 3To completely determine whether you have enough adapters, you'll need to figure out how many 4different ways they can be arranged. Every arrangement needs to connect the charging outlet to your 5device. The previous rules about when adapters can successfully connect still apply. 6 7The first example above (the one that starts with 16, 10, 15) supports the following arrangements: 8 9(0), 1, 4, 5, 6, 7, 10, 11, 12, 15, 16, 19, (22) 10(0), 1, 4, 5, 6, 7, 10, 12, 15, 16, 19, (22) 11(0), 1, 4, 5, 7, 10, 11, 12, 15, 16, 19, (22) 12(0), 1, 4, 5, 7, 10, 12, 15, 16, 19, (22) 13(0), 1, 4, 6, 7, 10, 11, 12, 15, 16, 19, (22) 14(0), 1, 4, 6, 7, 10, 12, 15, 16, 19, (22) 15(0), 1, 4, 7, 10, 11, 12, 15, 16, 19, (22) 16(0), 1, 4, 7, 10, 12, 15, 16, 19, (22) 17 18(The charging outlet and your device's built-in adapter are shown in parentheses.) Given the 19adapters from the first example, the total number of arrangements that connect the charging outlet 20to your device is [1m[37m8[0m. 21 22The second example above (the one that starts with 28, 33, 18) has many arrangements. Here are a 23few: 24 25(0), 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 17, 18, 19, 20, 23, 24, 25, 28, 31, 2632, 33, 34, 35, 38, 39, 42, 45, 46, 47, 48, 49, (52) 27 28(0), 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 17, 18, 19, 20, 23, 24, 25, 28, 31, 2932, 33, 34, 35, 38, 39, 42, 45, 46, 47, 49, (52) 30 31(0), 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 17, 18, 19, 20, 23, 24, 25, 28, 31, 3232, 33, 34, 35, 38, 39, 42, 45, 46, 48, 49, (52) 33 34(0), 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 17, 18, 19, 20, 23, 24, 25, 28, 31, 3532, 33, 34, 35, 38, 39, 42, 45, 46, 49, (52) 36 37(0), 1, 2, 3, 4, 7, 8, 9, 10, 11, 14, 17, 18, 19, 20, 23, 24, 25, 28, 31, 3832, 33, 34, 35, 38, 39, 42, 45, 47, 48, 49, (52) 39 40(0), 3, 4, 7, 10, 11, 14, 17, 20, 23, 25, 28, 31, 34, 35, 38, 39, 42, 45, 4146, 48, 49, (52) 42 43(0), 3, 4, 7, 10, 11, 14, 17, 20, 23, 25, 28, 31, 34, 35, 38, 39, 42, 45, 4446, 49, (52) 45 46(0), 3, 4, 7, 10, 11, 14, 17, 20, 23, 25, 28, 31, 34, 35, 38, 39, 42, 45, 4747, 48, 49, (52) 48 49(0), 3, 4, 7, 10, 11, 14, 17, 20, 23, 25, 28, 31, 34, 35, 38, 39, 42, 45, 5047, 49, (52) 51 52(0), 3, 4, 7, 10, 11, 14, 17, 20, 23, 25, 28, 31, 34, 35, 38, 39, 42, 45, 5348, 49, (52) 54 55In total, this set of adapters can connect the charging outlet to your device in [1m[37m19208[0m 56distinct arrangements. 57 58You glance back down at your bag and try to remember why you brought so many adapters; there must be 59[1m[37mmore than a trillion[0m valid ways to arrange them! Surely, there must be an efficient way 60to count the arrangements. 61 62[1m[37mWhat is the total number of distinct ways you can arrange the adapters to connect the 63charging outlet to your device?[0m 64 65