King Joseph once decided to test the intelligence of 3 of his ministers.
He gave them a list of the following words: VAT TOE PAD HOE OAR
1. Each of three ministers was told one letter of a certain word. Thus, each minister knew only one of the letters and also no two ministers knew the same letter.
2. The ministers were then informed that their three letters could be arranged to spell one of the words in the list given to them.
3. Each minister was then asked in turn, "Have you identified the word spelled by the letters"
The first minister answered in the affirmative. Then, the second minister answered yes and, finally, the last one also confirmed that he knew the word.
Which word did the letters spell? Provide a detailed explanation along with your answer.