= Solution
Number the epoxide-bearing ring <carbon> carrying CH$_2$OH as C1, then proceed through the other <epoxide> <carbon> C2 around the ring to C6. Heating with water opens the <epoxide> at the less substituted C2 by backside attack: the incoming <oxygen> becomes C2–OH on the front face, while the original <epoxide> <oxygen> remains as C1–OH on the back face. Proton transfers complete formation of the triol. Thus the two original <epoxide> <oxygens>' roles are distinct: one is retained from B and the new hydroxyl <oxygen> comes from water.
Iodine next activates the remaining C4=C5 bond as an iodonium <ion>. The pendant <primary alcohol> <oxygen> attacks intramolecularly at C5 to make the five-membered cyclic <ether> with path \b[O–CH$_2$–C1–C6–C5], opening the iodonium anti and leaving iodine at C4 on the opposite face. Bicarbonate removes the oxonium proton and neutralizes acid; it is not the source of the <ether> <oxygen>. The folded tether selects the face of closure compatible with the bridged structure, accounting for the <ether>/iodine <stereochemistry>.
The remaining two hydroxyl groups react with acid-activated 2,2-dimethoxypropane. Successive <oxygen> attack, methanol departure and intramolecular closure form the \b[isopropylidene <ketal>] of C, protecting that diol without changing its <carbon> configurations. The terminal primary hydroxyl has already become the cyclic <ether> and is not one of the two acetonide <oxygens>. This atom tracking distinguishes the <epoxide> <hydrolysis>, <iodoetherification> and protection stages.
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