|Spoiler Inside: Solution to Puzzle||SelectShow>|
Solve this problem by building a decision tree. (Wikipedia’s Decision Tree article) From the starting point, consider each of A, B, and C. No rules prevents these as one-letter words.
Taking the valid one-letter words, now consider what can be added to them to make valid two-letter words. AA yes, AB no, AC yes, BA no, BB yes, BC no, CA yes, CB yes, and CC yes.
Two to three: AA* – an asterisk means any letter – no, ACA yes, ACB yes, ACC yes, BB* no, CAA yes, CAB no, CAC yes, CBA no, CBB yes, CBC no, CCA no, CCB yes, and CCC no.
Three to four: ACAA yes, ACAB no, ACAC no, ACBA no, ACBB yes, ACBC no, ACCA no, ACCB yes, ACCC no, CAA* no, CACA yes, CACB yes, CACC yes, CCBA no, CCBB yes, and CCBC no.
Four to five: ACAA* no, ACBB* no, ACCBA no, ACCBB yes, ACCBC no, CACAA yes, CACAB no, CACAC no, CACBA no, CACBB yes, CACBC no, CACCA no, CACCB yes, CACCC no, and CCBB* no.
Five to six: ACCBB* no, CACAA* no, CACBB* no, CACCBA no, CACCBB yes, and CACCBC no.
Six to seven: CACCBB* no.
The longest possible word in Fauxgo is the six-letter word “CACCBB”.