Note: I never figured out the actual method to the letter clicking in step two of each puzzle. I was able to solve all three in a minute or two just by randomly clicking. Note: The "hint" menu will tell you 2 of the 4 letters that need to be selected.
Ockley
- Name letters: "Hortensius escaped the riots". "HORTENSIUS" minus "RIOTS" leaves "HENUS". Return to The Moon's Map and enter "HENUS" after "OCKLEY". Unscramble the new word: "HONEYSUCKLE".
- Puzzle screen: Select only these 4 letters from the word at the top of the screen: "R", "G", "T" and "T".
Ostheim
- Name letters: "Gardener had no reader". "GARDENER" minus "READER" leaves "GN". Return to The Moon's Map and enter "GN" after "OSTHEIM". Unscramble the new word: "SOMETHING".
- Puzzle screen: Select only these 4 letters from the word at the top of the screen: "E", "R", "E" and "N".
Olmstead
- Name letters: "Brighton dropped his thong and Molyneux squeezed his lemon". "BRIGHTON" minus "THONG" leaves "BRI", and "MOLYNEUX" minus "LEMON" leaves "YUX". Return to The Moon's Map and enter "BRI" and "YUX" after "OLMSTEAD". Unscramble the new word: "AMBIDEXTROUSLY".
- Puzzle screen: Select only these 4 letters from the word at the top of the screen: the first "E", the second "E", "G" and "N".
Final Step
Solving the 3 puzzles results in the following letters: "RGTTERENEEGN". Unfortunately, these don't make up a name or fit anywhere in Buckbee's grid. However, it is easily noticed that many of these letters are duplicated. Taking this into account along with the name hints in Buckbee's grid, we see one that reads "He is Irish and heeds only half". If we remove half of the letters (1 for each which has a duplicate), we are left with "RGTENE", which will fit into that column (#4). Unscramble this to "REGENT" and enter it into the "Buckbee" Puzzle on the Moon's Map.