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From the lower Strauchon Glacier gain the hanging glacier on the face via a narrow gully to the right of the glacier to reach a shingle rib, or use the Direttissima start up the buttress. Cross to the glacier and start 50m to the left of the Dilemma-Unicorn corner. Climb easily up to a huge arch and tend left into a left-facing corner. The corner runs all the way up the face, passing beside an overhang near the top, to finish on the ridge right of the summit. A sustained ~30 pitch climb with crux pitches of 15. Anchors are sometimes hard to find.
Some Update of details. DCF Feb 2021. We approached the hanging glacier from the waterfall that drains the western side of the hanging glacier. This route is prone to rockfall. We took the safer western side of the water fall. 5 pitches, with the second pitch having some good unprotected slab moves. Protection is thin. My advice is to use the Directissma approach which is less prone to rockfall. The only comfortable bivy sites are the hanging glacier (varies in size season by season) and at the col between Dilemma and Unicorn. The main face from the hanging glacier to the col is 24 pitches. About another 5 pitches to the summit. Climbing is about grade 13. Gear is thin, but it is there with some hard work. Rock is great. Water can be a problem but there is snow at the col.
Fred From, Murray Judge, Nic Kagan, Nov 1978.
The face from the glacier to
The face from the glacier to the top is 30 to 33 pitches using a standard 50m rope, and the rock grade is 15. Alpine rock grades by tradition have always been soft for a very good reason, except in the case of the Direct Dilemma route the grade is genuine 15 because it can be wet, and also it is normally climbed unroped.