One professor has written a 3-letter word on the blackboard, and explained that it was a 3-digit number in base 26, using A=0, B=1, C=2, etc.
A second professor figured what the decimal equivalent was, and then used the first professor's notation to write it: 0=A, 1=B, 2=C, etc.
He noticed that the result was also a common 3-letter word.
What were the two words?
The value of "bed" in base-26 is:
1*26^2 + 4*26+3 = 783
Therefore,in accordance with the second assignment, (7,8,3)=> (h,i,d).
Hence, 783 gives "hid".
Accordingly, the two words are "bed" and "hid".
An alternate answer is "alp" --> 0*26+11*26+15 = 301.
Now, 301 --> "dab"
Accordingly, the two words are "alp" and "dab"