Here are some letter string analogy problems from the Copycat project. These problems are a sample of the many hundreds or thousands of problems devised by various members of the Fluid Analogies Research Group, led by Douglas Hofstadter, currently at the Center for Research on Concepts and Cognition at Indiana University.

For a good introduction to the Copycat project, see Chapter 5 of Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought.

abc -> abd, ijk -> ?
abc -> abd, ijklmnop -> ?
abc -> abq, ijk -> ?
abc -> abd, iijjkk -> ?
abc -> abd, aabbcc -> ?
abc -> abd, hhwwqq -> ?
abc -> abcd, pqr -> ?
abc -> abd, abcd -> ?
abc -> abd, abcc -> ?
abc -> abd, cba -> ?
abc -> ac, pqr -> ?
abc -> abbc, pqr -> ?
abc -> abd, xcg -> ?
abc -> abd, pxqxrx -> ?
abcm -> abcn, rijk -> ?
abc -> abd, ace -> ?
abc -> abd, abacad -> ?
abc -> abd, mnmomp -> ?
abc -> abd, xaxbxc-> ?
abc -> abd, cacbcc -> ?
abc -> abcd, rqp -> ?
abc -> aabbcc, ppqqrr -> ?
a -> b, c -> ?
a -> aa, b -> ?
a -> ab, z -> ?
a -> z, b -> ?
abc -> abd, abcabc -> ?
abc -> abd, abcijk -> ?
abc -> abd, abcijkpqr -> ?
aabc -> aabd, ijkk -> ?
abc -> abd, lmnfghopq -> ?
abc -> abd, kji -> ?
abc -> abd, edc -> ?
a -> aa, pqr -> ?
ab -> aabb, pqrs -> ?
abc -> ac, pqrijk -> ?
abc -> ac, mmm -> ?
abc -> ac, mxg -> ?
aaabc -> c, xyzzz -> ?
abcd -> c, wxyz -> ?
pqfg -> fgpq, iiww -> ?
abc -> abd, azaza -> ?
abc -> abd, adddbddcd -> ?
abc -> abd, bcdacdabd -> ?
abc -> abd, wxyzxyzyz -> ?
abc -> abd, mrrjjj -> ?
abc -> abcd, abcdxfg -> ?
abc -> abcd, xyz -> ?
abc -> abd, rssttt -> ?
abc -> abd, xpqdef -> ?
abc -> abd, aababc -> ?
abc -> abd, mmnmno -> ?
abc -> abd, aaabbc -> ?
abc -> abd, xyz -> ?
abcdde -> abcde, pqstu -> ?
abced -> abcde, ppqqrrss -> ?
abcdfeg -> abcdefg, onmlkij -> ?
abc -> axc, nnn -> ?
aqc -> abc, pqc -> ?
abcc -> abcd, xyzz -> ?
pgzlrb -> pgzmrb, sizcq -> ?
pgzlrb -> pgzmrb, sicjz -> ?
pqr -> rqp, a -> ?
a -> pqr, z -> ?
a -> z, pqr -> ?
eqe -> qeq, abbbc -> ?