103

separate wire into two groups. 1 group has 1 wire, another group has 102 wires and number them with numbers from 1,2,,,,102. connect 102 wires that k wire connects k-1 and k+1 wires. Wire 1 only connects to wire 2 with two Rs and 101 wire connects only to 102.

In another room, measure 103 wires, the one not connected to any is 1 wire group. the wire has 2Rs but only connected to one wire is 1. then the one connects to 1 is 2. since 2 connects to 2 wires, so another connected to wire 2 is wire 3, ..... until you find 102.