Here is Cramer's solution:
The "challenged" does this: choose a random number in 1..1000, r, look up question number r for Komodo dragons and memorize it. The challenger then provides an unpredictable random number in 1..1000, c, and says "give me two answers, one from each list, where the question numbers add up to c modulo 1000. So the challenged calculates c - r (mod 1000) to get r2, which is the number of a question from the Fermat list, which he can immediately provide, along with the r-th Komodo dragon question, and the challenger veries that r + r2 = c mod 1000.
(For anyone interested, this is the extremely elegant solution to how to combine Sigma protocols in OR relations, "first" discovered in CDS-94 (see the first sections of my blog on ring signatures for details: https://reyify.com/blog/ring-signatures )