I actually finished this 3D puzzle a couple weeks ago, shortly after posting the all-but-one-piece photo on October 4 — http://365project.org/rhoing/365/2013-10-04 .
In the end, the solution is a bit “diabolical” (“very wicked or cruel; fiendish”).
It turns out that while the light-blue piece goes in last, the yellow piece cannot be pushed all-the-way-in. To insert the light-blue piece — and complete the sphere — the yellow piece must be partially backed-out. Although I characterize this feature of the solved puzzle as diabolical, it has an obvious advantage: the puzzle will not spontaneously come apart without deliberate human action.
Retired economics professor (“dismal scientist”). Married 40+ years to the love of my life; we have two grown daughters, both married, two granddaughters and a...