After a leisurely morning confirming that there's nothing much to do in Innsbruck, we took the cable car up to the Seegrube "Hotel" (really a hut, but with added towels). Since this was a rest day, we contented ourselves with a 4 hour walk with only 450m of ascent.
The next day started cloudy but dry, and we did the Innsbrucker Klettersteig, a grade 3 (out of 5) via ferrata which traverses the crest of the ridge above Innsbruck for a mile or two. This started as it meant to go on, with a steep (slightly overhanging) climb up metal rungs for about 10m. Things eased after this, but the expsosure was considerable, and some of the trickiest moves involved down-climbing.
About 2/3 of the way along, the klettersteig ends at a grassy col, offering the chance (which most people seemed to be taking) to escape back to the hut. But we were made of sterner stuff, so continued on our way. The route from here was more difficult but less exposed so we made good progress - until the sting in the tail that is, a 20m overhanging descent down metal rungs with an awkward wide step left at half height.
By now it had become a gloriously sunny day. From the end of the klettersteig we took a long (5 hour) route, descending steeply down scree before a wandering traverse along the Gilfelsturmerweg across grassy alps, before a final big ascent up to the Solsteinhaus hut. Another 11 hour day, great fun. The Solstein hut was much older than the others we'd stayed in, with lots of creaking timber, and without any hot water for washing. But it was superbly situated, with ridiculous amounts of excellent food, great atmosphere, and the warden even spoke excellent English; it was easily the best hut of the trip.
Our original plan had been to descend the next day and take the train to Imster to do a notoriously difficult grade 5 klettersteig. But a combination of poor weather forecasts, plus the unexpected difficulty of the Innsbrucker route (and also the fact that we were enjoying the area we were in so much), meant a change of mind. We decided to have another rest day, and therefore had a 10 hour epic ascending the Grosser Solstein (2541m) and Kleiner Solstein (2637m). The view east from here answered the question of why there was no marked route joining these summits to the Innsbrucker traverse, as the ridge continued in a series of huge vertical cliffs.
The following day was forecast to be very wet and windy, so we abandoned plans for a high level route to the next hut, in favour of a slightly lower and more sheltered path. However, the next morning we woke to blue skies, with valleys full of cloud, so quickly reverted to plan A and took the Freiung Hoehenweg to the Nordlinger Hut. The next few hours we enjoyed some of the best weather of the whole holiday, it was difficult to avoid the temptation of just sitting and looking. But on the assumption that the bad weather had been delayed rather than cancelled, we kept moving. We passed two Germans coming in the opposite direction, who made us realise that we weren't overloaded after all, as they wheezed by with rucksacks filled to bursting and assorted bits and pieces strapped to the outsides. We didn't have the heart to tell them it had taken us 5 hours to get to that point!
By now the clouds were beginning to roll in, and the last hour up to the hut were in thick mist. We got to the hut at about 2.30. Within half an hour the rain had started, and continued to get worse during the rest of the day with storms and gale force winds overnight. The Nordlinger hut was the highest we stayed in, on the summit ridge at almost 2400m. It was also one of the most basic in terms of facilities, with only (very) cold water, and no lights in the rooms to save electricity. Mind you, there was enough power available for the wardens to have a satellite TV on in the back room all evening!
The following morning, we walked down the long descending path back to the valley 1300m below, just in time to catch the train back to Innsbruck. After a wet day trip to Salzburg ("the hiiiiiiills are aliiiiive with the sound of muuuuusiiiiiiic") it was back to Munich.