(12 years ago) Very good puzzle. 8 tries.
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EDIT 2023, 22nd Feb. - bringing stars to this excellent level. Had quite some troubles to get rid of the last 4 steps (for 105)
I got stuck on the 4 off path and its variations for several tries. The steps to perform that cut are completely unintuitive, and I'm surprised that nobody commented on it. 8 tries.