Numerical evaluations of 2-loop kites and 3-loop tadpoles
with several elliptic obstructions lead to remarkable
empirical evaluations in terms of polylogarithms, for which
proofs are very hard to find, notwithstanding intensive use
of packages such as HyperInt and MZIteratedIntegral. I
describe the efficient methods by which puzzlingly simple
results were obtained and hopes for demystifying them.