At the summit we had a twenty minute break during which time the 'group of five' reached the top and continued just ahead of us. We set off shortly after them at 17:30pm and soon found ourselves ahead of them after they inadvertently headed up Sgurr a Fionn Choire. The snow that had only a couple of days previously threatened our attempt at the traverse had now virtually disappeared but as we skirted Am Bhastier we found ourselves walking through it on a well trodden path. Climbing up to Bealach a Bhasteir we came across a couple having a brew up. They told us that they had started the traverse of the ridge from Glen Brittle the day before but since we had not seem them we could only assume it must have been very early. Later we wondered if it had been them we had seen below us on the bealach between Thormaid and Ghreadaidh. They were planning to descend to Glen Sligachan, camp out and them complete the greater traverse by climbing Blabheinn and Clach Glas the following day. Also at the bealach were two rucksacks parked. We parked ours just as the 'group of five' arrived and did the same and set off up Am Bhasteir. We passed the owners of the two rucksacks whom, as we suspected, were the 'group of two'. We negotiated the bad step just as the 'group of five' caught up with us and eventually left hem to reach the top first so that we would have it to ourselves for photos and video. At 18:30pm we were on the summit with only one more summit to go. Back down to the bealach, pick up our rucksacks and then on towards Sgurr nan Gillean. We decided on what we believe to be Toothed Arete (moderate). David climbed it first without the rope but then insisted on throwing it down to me for which I was very thankful. Once at the top I continued, still roped, across a short awkward bit and then I belayed David whilst he crossed it. The 'group of five' were just descending having been to the summit already. They had left their sacks and gear below and were now faced with down-climbing. We offered the assistance of the rope abut they preferred to manage without. A short scramble and at 19:58pm we stood on top of Sgurr nan Gillean having completed the traverse of the ridge.