Explanation
To arrange the words in alphabetical order as they appear in a dictionary, we compare them letter by letter from left to right.
All five words begin with ga. Comparing the third letter of each word, Gaiety, Gain, Gainsay, and Gaiter have the letter i, while Gauge has the letter u. Since i comes before u in the alphabet, Gauge (5) is the last word in the sequence.
Next, we compare the four words starting with gai: Gaiety, Gain, Gainsay, and Gaiter. Comparing their fourth letters, Gaiety has e, Gain and Gainsay have n, and Gaiter has t. Alphabetically, e comes first, followed by n, and then t. Therefore, Gaiety (4) is the first word.
Comparing Gain (1) and Gainsay (3), both share the prefix gain. Since Gain (1) is shorter and is completely contained within Gainsay (3), Gain (1) comes first, followed by Gainsay (3).
Gaiter (2), with the fourth letter t, comes after Gainsay (3).
Combining these steps gives the final alphabetical sequence of 4, 1, 3, 2, 5.