Okay, so I need to figure out this organic chemistry problem. Let me start by breaking down the question step by step. The question is about a series of reactions starting with 1,3-dibromoadamantane and going through several steps, and then determining the coupling pattern in the 1H NMR of the final product. The choices are A to D, each being a different splitting pattern. 

First, the starting material is 1,3-dibromoadamantane. Heating this with excess KOH at 240°C gives product 1. Then, product 1 is heated with excess aluminum isopropoxide to form product 2. Next, ozone is bubbled through a solution of product 2 at -78°C, followed by adding dimethylsulfide (DMS) to get product 3. The question is about the coupling pattern of the most deshielded hydrogen in product 3's 1H NMR spectrum.

Let me start by analyzing each step one by one. 

First reaction: 1,3-dibromoadamantane + KOH (excess) → product 1. I know that when vicinal dihalides (like 1,2-dibromides) are treated with excess base, they undergo elimination reactions. But here, the starting material is 1,3-dibromoadamantane. Adamantane is a diamondoid structure, a type of polycyclic hydrocarbon. The structure of adamantane is a bridge structure with two bridgeheads. So, 1,3-dibromoadamantane would have bromine atoms on two bridgehead carbons. 

When a vicinal dihalide (but here it's 1,3, so not quite vicinal) is treated with a strong base like KOH, elimination reactions can occur. However, in adamantane derivatives, the bridgehead positions are sterically hindered. Vicinal dihalides can lose two equivalents of HX (here, HBr) to form an alkene via an E2 mechanism. But since the starting material is 1,3-dibromoadamantane, the two bromines are on bridgehead carbons that are not adjacent. So, would elimination even be possible here? Or maybe it's a different kind of reaction.

Wait, another possibility is that the base (KOH) could cause a substitution reaction. Since there are two bromine atoms, maybe each bromide undergoes substitution. But in a rigid structure like adamantane, substitution might not be straightforward. Alternatively, perhaps it's an elimination reaction. Let me think. 1,3-dibromoadamantane could eliminate two molecules of HBr to form a double bond. But where? Since the bromines are on 1 and 3 positions, the elimination would form a double bond between carbons 1 and 2, or 2 and 3? Wait, the structure of adamantane is such that positions 1 and 3 are adjacent in a certain way. Let me recall the structure. Adamantane has a structure with two bridgeheads, positions 1 and 3, and other bridge positions. So, maybe the elimination would form a double bond between C1 and C2, producing a 1,2-diene? But I'm not entirely sure. Alternatively, perhaps the two bromines are on adjacent bridgeheads, allowing for elimination to form a double bond between them.

Wait, maybe the starting material is 1,3-dibromoadamantane, but upon heating with KOH, it undergoes a double elimination to form a diene. Let me check the possible product. The IR spectrum of product 1 has a peak at 1720 cm⁻¹, which is characteristic of a carbonyl group. Wait, but wait—1720 cm⁻¹ is a strong absorption for a carbonyl, but in the starting material, there are two bromines. If elimination occurs, perhaps forming a carbonyl. Wait, but elimination usually forms double bonds. Hmm. Alternatively, maybe substitution occurs. Let me think again.

Wait, another possibility: the starting material is 1,3-dibromoadamantane, which upon treatment with KOH (a strong base) might undergo an E2 elimination. Since the two bromines are on 1 and 3 positions, perhaps they are not adjacent, so elimination might not be straightforward. Alternatively, maybe the base abstracts a β-hydrogen from one bromide, leading to the formation of a double bond. But if the two bromines are not adjacent, this might not form a double bond. Alternatively, maybe the two bromides are on adjacent carbons? Wait, the question says 1,3-dibromoadamantane. Adamantane has bridgehead positions 1 and 3. So, positions 1 and 3 are connected by a bridge, so they are not adjacent. Hence, adjacent carbons would be positions 1 and 2, 2 and 3, etc. So, 1 and 3 are not adjacent. Therefore, elimination between 1 and 3 would require breaking a bridge, which is possible? But that would require a bridge cleavage, which might not occur easily. 

Alternatively, perhaps the reaction is a substitution. Since there are two bromines, maybe each Br is replaced by OH (from KOH). But in a rigid structure like adamantane, substitution might not be feasible. Alternatively, maybe the two bromines are undergoing elimination, but in a way that forms a carbonyl group. Wait, the IR spectrum of product 1 shows a peak at 1720 cm⁻¹, which is a strong carbonyl (C=O) stretch. So if product 1 has a carbonyl group, that suggests that there's a ketone or aldehyde formed. So, how could elimination from 1,3-dibromoadamantane lead to a carbonyl?

Wait, maybe the reaction is a dehydrohalogenation followed by oxidation? But KOH is a base, not an oxidizing agent. Alternatively, perhaps the elimination forms a double bond, and then oxidation occurs. But the question states that product 1 is formed by heating with KOH. Alternatively, maybe the two bromines are on bridgehead positions, and the elimination leads to a bridge being broken, forming a carbonyl group. 

Alternatively, perhaps the reaction is a substitution. Each Br is replaced by OH, forming 1,3-dihydroxoadamantane. But then, in the IR spectrum, a carbonyl peak would not be present. So that's inconsistent. Therefore, elimination must be happening to form a carbonyl. 

Wait, maybe the elimination is a double elimination. Let me think: if we have 1,3-dibromoadamantane, perhaps two elimination steps occur. Each elimination step removes HBr and forms a double bond. But how would that lead to a carbonyl? Alternatively, perhaps the base abstracts a β-hydrogen from one Br, leading to the formation of a double bond adjacent to the other Br. Then, perhaps an oxidation occurs to form a ketone. But the question states that product 1 is formed with KOH. If oxidation is needed, that would require an oxidizing agent, but KOH is a base. Unless the base is causing dehydrohalogenation followed by some rearrangement.

Alternatively, maybe the starting material is 1,3-dibromoadamantane, and the base (KOH) causes elimination to form a conjugated diene. But then the IR wouldn't show a carbonyl. So maybe that's not it. 

Wait, another angle: the product's 1H NMR shows a peak at 4.79 ppm, which is a triplet (2H), then a multiplet (10H), and another triplet (2H). The IR at 1720 suggests a carbonyl group. So product 1 is likely a ketone. So how can 1,3-dibromoadamantane form a ketone with KOH? Maybe the bromines are on adjacent carbons, and elimination forms a carbonyl. Wait, but the starting material is 1,3-dibromoadamantane. Maybe the structure is such that the two bromines are on bridgehead carbons that are adjacent. Wait, no, in adamantane, bridgeheads are not adjacent. So perhaps the structure is such that upon elimination, a carbonyl forms. Alternatively, maybe the starting material is not 1,3, but perhaps 1,2-dibromoadamantane. Wait, the question says 1,3-dibromoadamantane. Hmm.

Alternatively, maybe the base causes a substitution. For example, each bromide is replaced by an OH group, forming 1,3-diol. But then the IR would not have a carbonyl. So that's not matching. 

Wait, perhaps the reaction is a double elimination. Let's suppose that in 1,3-dibromoadamantane, each Br is on a bridgehead. When KOH is added, the base abstracts a β-hydrogen, leading to elimination of HBr and formation of a double bond. But since the two Brs are on non-adjacent carbons, maybe elimination occurs at both ends, leading to a conjugated diene. But then the IR wouldn't have a carbonyl. Alternatively, maybe one elimination gives an alkene, and another elimination gives a ketone? That seems unlikely. 

Alternatively, perhaps the reaction is a ring-opening. Adamantane has bridge rings. If the two bromines are on bridgeheads, maybe the base causes cleavage of the bridge, leading to a six-membered ring or something else. But then, how would that form a carbonyl group? 

Wait, maybe the reaction is an example of a Criegee mechanism or some kind of oxidation. But KOH is a base, not an oxidizing agent. Hmm. 

Alternatively, perhaps the starting material is not 1,3-dibromoadamantane, but rather 1,2-dibromoadamantane. If that's the case, then elimination would form a double bond, and perhaps further reaction. But the question states 1,3. 

This is confusing. Let me try to look up what 1,3-dibromoadamantane would look like. Upon a quick mental note, adamantane has a structure with two bridgeheads. So, positions 1 and 3 are the bridgeheads. The other positions are bridge positions. So, 1,3-dibromoadamantane would have bromines on both bridgeheads. Now, heating with KOH. Let's think of possible reactions.

In such a structure, elimination would require breaking a bridge. Since bridgeheads are connected by bridges, perhaps the elimination would lead to a ring opening, forming a smaller ring. For example, breaking a bridge to form a five-membered ring. But how would that form a carbonyl group? Alternatively, maybe the elimination forms a conjugated diene, but again, no carbonyl.

Wait, another angle: the IR peak at 1720 suggests a carbonyl group. Which carbonyl groups absorb around 1720? Aldehydes and ketones. So, product 1 must have a ketone or aldehyde group. How can that form from 1,3-dibromoadamantane?

Maybe the two Br atoms are not on the same bridgehead but adjacent ones. Wait, but the naming is 1,3-dibromoadamantane. So, positions 1 and 3 are the bridgeheads. Let me imagine the structure. Adamantane has a structure with two bridgeheads (positions 1 and 3) connected by bridges. The other positions (like 2, 4, etc.) are bridge positions. So, if 1 and 3 are bridgeheads, then positions 2 and 4 are connected via a bridge. 

So, if we have 1,3-dibromoadamantane, the Brs are on positions 1 and 3. Now, when KOH is added, perhaps each Br is converted into a carbonyl group. Wait, but that would require oxidation. But KOH is a base, not an oxidizing agent. So maybe some kind of elimination followed by oxidation. Alternatively, maybe the reaction is a ketonization. 

Alternatively, maybe the base causes the two Br atoms to leave, forming a double bond. But since the two Brs are on bridgeheads, which are not adjacent, elimination would require breaking a bridge. For example, breaking the bridge between 1 and 2, or 3 and 4. Let's say the bridge between 1 and 2 is broken, leading to a double bond between 1 and 2. But then, would that form a carbonyl? 

Wait, maybe the elimination forms a carbonyl group. For example, if a double bond forms between two adjacent carbons, and then one of them is oxidized to a carbonyl. But again, the question states that the reaction is with KOH, which is a base, not an oxidizing agent. 

Alternatively, perhaps the two Brs are on adjacent bridgehead positions. Wait, but the name is 1,3-dibromoadamantane, so that's not possible. So, perhaps the structure is such that elimination forms a conjugated diene, and then one of the carbons is deprotonated and a carbonyl forms. But I'm not sure. 

Alternatively, maybe the reaction is a ring-opening metathesis, but that's more likely with metals like Grubbs catalyst. 

Wait, maybe the reaction is a pinacol coupling. But pinacol coupling involves vicinal diols, which isn't the case here. 

Alternatively, perhaps the reaction is a double elimination to form a carbonyl. Let me think: if each Br leaves, and the adjacent hydrogens are abstracted, forming a double bond. But with two Brs, perhaps two eliminations occur. If the two eliminations occur, forming two double bonds, but in a rigid structure like adamantane, that's not feasible. 

Alternatively, maybe the two Br atoms are on adjacent carbons, but the name 1,3 suggests they are not. So, perhaps the reaction forms a conjugated diketone. But that would require oxidation. 

Wait, perhaps I'm overcomplicating this. Let's think about product 1's NMR. The NMR shows a triplet at 4.79 ppm (2H), a multiplet (10H), and another triplet (2H). The IR shows a carbonyl. So, product 1 is likely a ketone, perhaps with a bridge structure. For example, a bicyclic ketone. 

If product 1 is a ketone, then perhaps the starting material undergoes a ring-opening elimination to form a ketone. For example, if the bridge is broken, leading to a six-membered ring with a ketone group. But how? 

Alternatively, maybe the reaction is a [2+1] cycloelimination, but that's more common in enolate chemistry. 

Alternatively, perhaps the reaction is a retro-Diels-Alder, but that's unlikely here. 

Wait, another thought: maybe the starting material is 1,3-dibromoadamantane, and upon heating with KOH, it undergoes a double elimination to form a conjugated diene. Then, perhaps an oxidation occurs to form a diketone. But again, the question states that the reaction is with KOH, not an oxidizing agent. 

Hmm. Alternatively, perhaps the reaction is a ring-opening to form a carbonyl. For example, the bridge breaks, and the adjacent carbons form a carbonyl group. But how? 

Wait, maybe the reaction is a substitution where each Br is replaced by a hydroxyl group, forming a diol. But then, how does the carbonyl form? Unless there's some rearrangement. 

Alternatively, perhaps the reaction is a conjugate elimination. For example, the base abstracts a β-hydrogen leading to elimination of HBr and formation of a double bond. If there are two Brs, maybe two such eliminations occur, but in this case, the two Brs are on bridgeheads. 

Wait, maybe the reaction forms a bridgehead ketone. For example, if the bridge is broken, leading to a ketone at a bridgehead. But in adamantane, bridgeheads are sp³ hybridized, so how would a ketone form there? Unless the bridge is broken, and the adjacent carbon becomes a carbonyl. 

Alternatively, perhaps the reaction is a single elimination, forming a double bond, and then a carbonyl forms via oxidation. But the question says the reaction is with KOH, which would be a base, not an oxidizing agent. 

This is getting a bit stuck. Let me try to approach it differently. Let's look at the final product's NMR. The most deshielded hydrogen would likely be a proton adjacent to the carbonyl group. In a ketone, the alpha protons are deshielded. So, the coupling pattern would depend on how many neighboring protons they have. 

If the most deshielded proton is adjacent to a carbonyl group and has two neighboring protons, perhaps it's a triplet of triplets. Wait, but let's think. Suppose the structure is a bicyclic ketone. The carbonyl is at a bridgehead. The protons next to the carbonyl would be on adjacent bridge positions. Let's say the carbonyl is at position 1, then position 2 has two protons. Those protons would each be adjacent to the carbonyl (position 1) and to each other (positions 2). So each proton would be split by two neighboring protons (on position 2) and by the protons on position 1 (if any). Wait, but in a rigid structure like adamantane, the positions adjacent to the carbonyl may have two equivalent protons. 

Alternatively, perhaps the most deshielded proton is part of a bridgehead, adjacent to the carbonyl. Let's say the carbonyl is at position 1, and positions 2 and 4 (if any) are adjacent. Wait, but the exact structure is a bit tricky. 

Alternatively, perhaps the most deshielded proton is part of a chain leading to the carbonyl. For example, if the ketone is in a position with adjacent CH2 groups. Then, the protons on the CH2 next to the carbonyl would be split by the adjacent CH2. 

Wait, but let's consider an example. Suppose product 1 is a bicyclic ketone, such as a bicyclo[2.2.2]octanone derivative. The carbonyl is at a bridgehead. The adjacent carbons would have CH2 groups. For example, the ketone is at position 1, and the adjacent carbons (positions 2 and 3) each have two protons. Then, the protons on position 2 would be adjacent to the carbonyl (position 1) and to the protons on position 3. 

Wait, but in that case, the protons on position 2 would be split by the protons on position 3 and by the protons on position 1. However, the protons on position 1 (carbonyl) are deshielded and do not split the neighboring protons. 

Alternatively, maybe the most deshielded proton is on a CH group adjacent to the carbonyl. For example, if the structure is (CH2)2CO, then the protons on the CH2 next to CO would be split by the neighboring CH2. But in a rigid structure like adamantane, the adjacent protons might be equivalent. 

Wait, perhaps the most deshielded proton is part of a CH2 group adjacent to the carbonyl. Let's say the structure is something like:

          O
           \
            C-CH2-CH2-CH2-CH2-...

But in a bicyclic system, the adjacent carbons might have two protons each. 

Alternatively, maybe the structure is such that the most deshielded proton is part of a CH2 group next to the carbonyl, and each of these protons is split by the two protons on the adjacent carbon. For example, if the carbonyl is at position 1, then position 2 has two protons (a CH2 group), and position 2's protons are adjacent to position 1's carbonyl and to each other. So each proton on position 2 would be split by the two protons on position 2 and by the protons on position 1. Wait, but position 1 is a carbonyl carbon, which has no protons. So the splitting would come from the adjacent CH2 group. 

Wait, if position 2 is a CH2 group adjacent to the carbonyl, then each proton on position 2 would be split by the two protons on position 2 (since they are adjacent and equivalent) and by the protons on position 3. Wait, but position 3 might not be adjacent. 

Alternatively, maybe the structure is such that the most deshielded proton is part of a -CH2-CO- group, and the adjacent CH2 group has two protons. So the proton on the -CH2- next to CO would be split by the two protons on the adjacent CH2. Therefore, each of these protons would have two neighboring protons (from the adjacent CH2), leading to a triplet. But wait, the proton on the -CH2- next to CO would have two neighboring protons (from the adjacent CH2 group), so that would be a triplet. However, if the adjacent group has two protons, then each of the protons on the CO adjacent CH2 would be split into a triplet. But wait, the adjacent group has two protons, which are equivalent. So each proton on the CO-adjacent CH2 would see two neighboring protons (each from the adjacent CH2), but since the adjacent group has two equivalent protons, the splitting would be a triplet (n+1, where n=2). 

But the question mentions the coupling pattern of the most deshielded hydrogen. Let me think again. The most deshielded hydrogen is likely the one adjacent to the carbonyl group. Let's say it's on a CH2 group. Each proton on that CH2 would be split by the protons on the adjacent CH2 group. If the adjacent CH2 group has two protons, then each proton on the CO-adjacent CH2 would be split into a triplet (n=2, so 2+1=3). However, if there are more neighboring groups, maybe it's a more complex splitting. 

Alternatively, maybe the most deshielded proton is part of a geminal di-substitution. Wait, but geminal protons are on the same carbon. 

Wait, perhaps the structure after elimination and oxidation is a diketone. But no, the IR shows a single carbonyl. 

Alternatively, maybe the product is a bicyclic ketone. Let's imagine the structure as a bicyclo[2.2.1]heptanone. In such a structure, the ketone is at a bridgehead, and the adjacent carbons are CH2 groups. Then, the protons on those CH2 groups would be split by the protons on adjacent carbons. 

For example, consider bicyclo[2.2.1]heptan-2-one. The ketone is at position 2, and the adjacent carbons (positions 1 and 3) have two protons each. The protons on position 1 would be adjacent to the ketone (position 2) and to the protons on position 3. However, position 3's protons would be split by position 4's protons, etc. 

Wait, but the key is the coupling pattern of the most deshielded proton. Let's say the most deshielded proton is on a CH2 group adjacent to the ketone. Each of those protons would be split by the protons on the adjacent CH2 group. If the adjacent CH2 group has two protons, then each proton would split into a triplet. But if there's another splitting from another group, like from the bridgehead, which has no protons, then the coupling would only come from the adjacent CH2. 

Alternatively, maybe the structure is such that the most deshielded proton is part of a -CH- group adjacent to the carbonyl. But in a rigid structure, that might not be the case. 

Alternatively, perhaps the most deshielded proton is part of a -CH2- group adjacent to the carbonyl, and each of those protons is split by the two protons on the adjacent carbon. So each proton would have two neighboring protons, leading to a triplet. However, if there are two adjacent protons, each from a different direction, maybe it's a triplet of triplets. 

Wait, let me think of an example. Suppose the structure is:

      O
       \
        C-CH2-CH2-...

If the carbonyl is at position 1, then the adjacent CH2 (position 2) has two protons. Each of these protons would be split by the two protons on position 3 (if any). Wait, but position 3 may not be adjacent. 

Alternatively, if the structure is such that the most deshielded proton is part of a -CH2- group adjacent to the carbonyl, and each of those protons is split by the two protons on the adjacent carbon. For example, if the adjacent carbon has two protons, then each proton would split into a triplet. But if there's another adjacent group with protons, it would be a triplet of triplets. 

Wait, another angle: if the most deshielded proton is on a carbon adjacent to the carbonyl and has two neighboring protons (from another adjacent carbon), then the splitting would be a triplet of triplets. For example, if the structure is:

      O
       \
        C-CH2-CH(CH2...)

In this case, the proton on the CH2 next to the carbonyl would be adjacent to two protons (from the CH2 group) and perhaps another proton from a neighboring group. But I'm not sure. 

Alternatively, perhaps the most deshielded proton is part of a -CH2-CO- group, and each of those protons is adjacent to two protons (from the adjacent carbon). If the adjacent carbon has two protons, then each proton on the -CH2- would split into a triplet. But if there are two adjacent groups each contributing two protons, then it would be a triplet of triplets. 

Wait, the answer choices are: A. triplet of triplets (5), B. pentet (5), C. triplet (2), D. doublet of triplets (9). 

If the splitting comes from two different sets of neighboring protons, each contributing two protons, then the splitting would be a triplet of triplets, which would be 3×3=9 peaks (a nonet), but that's not an option. Alternatively, if each proton is split by three equivalent protons, it would be a quartet. 

Wait, perhaps the splitting is due to two different coupling partners. For example, each proton is split by two protons from one group and two protons from another group. But in reality, that would lead to a quintet (n=4, 5 peaks). But the options don't have quintet. 

Alternatively, maybe each proton is split by three protons. For example, if there are three neighboring protons, it would be a quartet. But the options don't have that. 

Alternatively, if a proton is split by two different sets of protons, each contributing two couplings. For example, two adjacent groups each with two protons. Then, the splitting would be a triplet (from two protons) plus another triplet, leading to a triplet of triplets (9 peaks), which is option A. 

But how would that happen? Let's imagine the structure. Suppose the most deshielded proton is on a CH2 group adjacent to the carbonyl. The adjacent carbon (position 2) has two protons. Those two protons are equivalent, so each proton on the CO-adjacent CH2 would split into a triplet. However, if there's another adjacent group (say, position 3) with two protons that are not equivalent, then the splitting would be more complex. 

Alternatively, maybe the structure has a geminal di-substitution. Wait, geminal protons are on the same carbon. 

Alternatively, perhaps the most deshielded proton is part of a -CH- group that's adjacent to the carbonyl and has two neighboring protons. For example, if the structure is:

      O
       \
        C-CH-CH2...

Then, the proton on the -CH- would be adjacent to the carbonyl (position 1) and to the -CH2- group (positions 3 and 4). If the -CH2- group has two protons, then the -CH- proton would be split by the two protons on the -CH2- group and perhaps another proton from the adjacent carbon. But this is getting too speculative. 

Alternatively, maybe the most deshielded proton is part of a -CH2-CH2- group adjacent to the carbonyl. Each proton on the -CH2- would be split by the two protons on the adjacent -CH2- group. So each proton would have two neighboring protons (from the adjacent -CH2-), leading to a triplet. But if there's another coupling, say from a bridgehead, which has no protons, then it's a simple triplet. 

But the question states that the coupling pattern is for the most deshielded hydrogen, excluding those that will exchange with deuterated solvent. So, perhaps the most deshielded proton is part of a CH2 group adjacent to the carbonyl, and each of those protons is split by the two protons on the adjacent CH2 group. That would make a triplet. But if there are two adjacent CH2 groups, each contributing two protons, then each proton would be split by two sets of two protons, leading to a triplet of triplets (9 peaks), which is option A. 

Wait, but how would there be two adjacent CH2 groups? Unless the structure is such that the most deshielded proton is part of a -CH2- group adjacent to the carbonyl and also adjacent to another -CH2- group. For example, in a structure like:

      O
       \
        C-CH2-CH2-

In this case, the protons on the first -CH2- would be adjacent to the carbonyl and to the second -CH2-. Each proton on the first -CH2- would be split by the two protons on the second -CH2- group. So each proton would see two neighboring protons, leading to a triplet. But if the first -CH2- group has two protons, then each of those protons would be split by the second -CH2- group's two protons. So, the splitting would be a triplet (n=2). But wait, if the first -CH2- group has two protons, each of those protons would be split by the two protons on the second -CH2- group. So each proton on the first -CH2- would have two neighboring protons (from the second -CH2-), leading to a triplet. But since the first -CH2- group has two equivalent protons, the splitting for each would be a triplet. So the coupling pattern would be a triplet. 

But wait, if the first -CH2- group is adjacent to the carbonyl and the second -CH2- group is adjacent to the first, then the splitting would be a triplet. However, if there's another coupling from the bridgehead, which has no protons, then the splitting remains a triplet. 

But the answer options include a triplet (option C) and a triplet of triplets (option A). So, perhaps there's a case where a proton is split by two different sets of two protons. For example, if the most deshielded proton is adjacent to two different CH2 groups, each with two protons. Then, each set of two protons would cause a splitting, leading to a triplet of triplets. 

Alternatively, maybe the structure is such that the most deshielded proton is part of a -CH2- group adjacent to the carbonyl, and each of those protons is also adjacent to another -CH- group with two protons. Then, each proton would be split by two different sets of two protons, leading to a triplet of triplets. 

But without the exact structure, it's challenging to be precise. However, based on the answer choices, the most common splitting for a proton adjacent to a carbonyl group is a triplet. But if there are two adjacent groups each causing a coupling, it could be a triplet of triplets. 

Alternatively, perhaps the structure after elimination and oxidation is a bicyclo[2.2.1]heptanone. The ketone is at position 2, and the adjacent carbons (positions 1 and 3) have two protons each. The protons on position 1 (adjacent to the ketone) would be split by the two protons on position 3. But position 3's protons are adjacent to position 4, which might not be adjacent to the ketone. 

Alternatively, perhaps the most deshielded proton is on a -CH- group adjacent to the carbonyl, with two neighboring protons. For example, in a structure like:

      O
       \
        C-CH-

If the -CH- group has two protons, each of those protons would be adjacent to the carbonyl (C=O) and to another CH2 group. Wait, but in this case, the protons on the -CH- would be split by the protons on the adjacent CH2 group. If the adjacent CH2 has two protons, then the splitting would be a triplet. 

But perhaps there's another adjacent group. For example, if the structure is such that the most deshielded proton is on a -CH- group adjacent to the carbonyl and also adjacent to another -CH- group. Then, each proton would be split by two different sets of protons. For example, if the adjacent groups each have two protons, the splitting would be a triplet of triplets. 

Alternatively, maybe the most deshielded proton is part of a -CH2-CH2- group adjacent to the carbonyl. Each proton on the -CH2- would be split by the two protons on the adjacent -CH2- group, leading to a triplet. But if there's another coupling from a different group, it would be more complex. 

Given the answer choices, and considering that the splitting is likely due to two adjacent protons, the most probable coupling pattern would be a triplet of triplets (option A). However, another possibility is that the splitting comes from three equivalent protons, leading to a quartet. But that's not an option. 

Alternatively, if the most deshielded proton is part of a -CH2- group adjacent to the carbonyl, and each of those protons is split by two protons from another adjacent group, leading to a triplet of triplets. 

But I'm not entirely sure. Let me try to think of a specific example. Suppose the product 1 is bicyclo[2.2.1]heptan-2-one. The structure would have a ketone at position 2, with adjacent carbons at positions 1 and 3. Each of these adjacent carbons would have two protons. The protons on position 1 would be adjacent to the ketone (position 2) and to the protons on position 3. Each proton on position 1 would be split by the two protons on position 3, leading to a triplet. However, if there's another adjacent group, like position 4, which also has two protons, then the splitting would be more complicated. 

Alternatively, perhaps the structure is such that the most deshielded proton is part of a -CH2- group adjacent to the ketone, and each of those protons is split by the two protons on the adjacent carbon, leading to a triplet. But if there are two such adjacent groups (each with two protons), then the splitting would be a triplet of triplets. 

But without the exact structure, it's hard to be precise. However, considering the answer choices and the most common splitting for protons adjacent to a carbonyl group, I would lean towards a triplet of triplets if there are two different sets of couplings. 

Alternatively, perhaps the most deshielded proton is split by three equivalent protons, leading to a quartet. But that's not an option. 

Alternatively, maybe the splitting is due to three different protons, but that's not one of the options. 

Alternatively, perhaps the most deshielded proton is part of a -CH- group adjacent to the carbonyl and has two neighboring protons, leading to a triplet. 

But the answer options have a triplet (option C) and a triplet of triplets (option A). 

Another angle: in the final product, product 3, the most deshielded hydrogen is after a series of reactions. Let's think about the reactions again. 

Product 1 is formed by heating 1,3-dibromoadamantane with KOH. Then, product 1 is heated with aluminum isopropoxide, forming product 2. Then, product 2 is reacted with dimethylsulfide (DMSD) in a solution at -78C, followed by dimethylsulfide, forming product 3. 

Wait, aluminum isopropoxide is often used as a reducing agent, perhaps in the formation of esters or ketones. But KOH is a strong base, so maybe the first step is elimination. Then, product 1 is a ketone. Then, product 1 is treated with aluminum isopropoxide. Aluminum isopropoxide can act as a reducing agent, perhaps reducing the ketone to an alcohol. But then, product 2 would be a secondary alcohol. 

Then, product 2 is treated with dimethylsulfide. DMSD is a reagent that can form sulfides. In the presence of a base, it can deprotonate the alcohol to form an alkoxide, which then reacts with DMSD to form a sulfide. The conditions are at -78C, which is liquid nitrogen temperature, used to prevent side reactions. 

So, the reaction would be: R-OH + DMSD → R-S + H2O, under basic conditions. 

So, if product 1 is a ketone, then product 2 would be the corresponding secondary alcohol. Then, reacting with DMSD would form a sulfide. 

But the IR of product 1 shows a carbonyl, so product 1 is a ketone. Then, product 2 is the secondary alcohol. Then, product 3 is the sulfide. 

So, the final product is a sulfide. The sulfide would have the structure where the ketone (from product 1) is converted to a sulfide. 

Now, considering the structure of product 3, the most deshielded hydrogen would likely be adjacent to the sulfur atom. Sulfides have a sulfhydryl group (-S-). The hydrogen adjacent to sulfur would be deshielded. The coupling pattern would depend on the neighboring protons. 

If the sulfide is attached to a carbon that is adjacent to another carbon with protons, the splitting would depend on the number of neighboring protons. For example, if the sulfide is attached to a carbon that is adjacent to a CH2 group, then the hydrogen on the sulfide carbon would be split by the protons on the adjacent carbon. 

Wait, but the sulfide group is -S-R. The hydrogen adjacent to sulfur would be on the carbon next to sulfur. If that carbon has two protons, then each of those protons would be adjacent to the sulfur, but the splitting would come from neighboring groups. 

Alternatively, the sulfide carbon (the one attached to sulfur) might have two protons. Then, the most deshielded hydrogen would be those protons. The splitting would depend on the neighboring groups. If the adjacent carbon has two protons, then each of those protons would be split by the two protons on the adjacent carbon, leading to a triplet. But if there are two adjacent groups each with two protons, it could be a triplet of triplets. 

Alternatively, if the sulfide carbon is attached to a bridgehead, which has no protons, then the splitting would come from the adjacent bridgehead's protons. But bridgeheads in adamantane don't have protons. 

Alternatively, perhaps the sulfide is part of a ring structure. For example, a disulfide bridge. But the reaction uses DMSD, which forms a single sulfide. 

Alternatively, perhaps the final product is a disulfide. But the problem states that product 3 is formed by reacting product 2 with DMSD, which would form a single sulfide. 

Wait, but the question says "excluding those that will exchange with deuterated solvent". So, the most deshielded hydrogen would be the one that's part of the sulfide group. 

In the sulfide group, the hydrogen adjacent to sulfur (if any) would be deshielded. For example, if the structure is R-S-R', where R and R' are alkyl groups. If the carbon attached to sulfur has two protons, then each of those protons would be split by the protons on the adjacent carbon. 

But the answer choices are triplet, pentet, triplet of triplets, or doublet of triplets. 

If the most deshielded hydrogen is on a carbon adjacent to the sulfur, and that carbon has two protons, then each of those protons would be split by the protons on the adjacent carbon. If the adjacent carbon has two protons, then each proton would split into a triplet. If there are two adjacent groups each with two protons, the splitting would be a triplet of triplets (9 peaks). 

Alternatively, if the most deshielded hydrogen is on a carbon that is part of a ring and has two neighboring protons, leading to a triplet. 

But considering the possible structures, the most probable splitting pattern is a triplet of triplets (option A) if there are two different sets of two protons each causing splitting. Alternatively, if there's only one set of two protons, it's a triplet (option C). 

But given the answer choices and the typical splitting patterns, I think the correct answer is a triplet of triplets (option A). However, I'm not entirely sure. Alternatively, maybe the splitting is due to three equivalent protons, but that's not an option. 

Another angle: the most deshielded hydrogen is part of a bridgehead. But bridgehead protons are usually not split because there are no adjacent protons. However, if the bridgehead has a substituent with protons, then the splitting would occur. 

Alternatively, if the most deshielded hydrogen is on a carbon adjacent to the sulfide group and has two neighboring protons, each from different groups, leading to a triplet of triplets. 

Given all this, I'll go with option A: triplet of triplets.
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