Langford pairings are sequences in which a set of N pairs, {1, 1, 2, 2, …, N, N}, is arranged so that every pair, {k, k}, appears in the sequence with k numbers between the pair. Langford pairings have been actively studied by mathematicians since the 1960s for their applications in computing, graph theory, and combinatorics. The purpose of this Math Circle activity is to explore Langford pairings for small values of N, leading to a justification for why solving the puzzle with certain values of N is impossible. The activity is made more approachable through the use of colored blocks (Unifix cubes) to represent the pairs of numbers.