What is the fewest number of steps (changing one letter at a time, with each step yielding a common English word) in which you can change "HOT" into "AIR" and then "AIR" into "BAG"?
This is the fewest number of steps. To make either change in three steps, each step would, of course, have to add one of the three letters of the second word. AOT, HOR, BIR, AAR, and AIG are all not words, so it will require at least one extra step to find those letters. HIT is, but neither AIT nor HIR is a valid word, so we still need the extra step.
Other, equivalent solutions were suggested in the problem comments.
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