To estimate a maximum purchase price for the coin that is going to be auctioned, let's consider several factors:

1. Condition: The coin in question has a condition rating of 110 (FDC), indicating that it is in exceptional condition. This generally translates to a higher price compared to coins of lower condition.

2. Previous auction prices: By observing the hammer prices from previous auctions, we can see that high-condition coins have reached hammer prices that vary, but are generally in the range of 5000 to 7000 euros. For example:
- In 2020, a coin with a starting price of 3000 euros reached a hammer price of 5000 euros.
- In 2015, a coin with a starting price of 6000 euros reached a hammer price of 6000 euros.
- In 2021, a coin with a condition rating of 100 was hammered at 4000 euros.

3. Starting price and average hammer price: The current starting price is 3500 euros, and the average hammer price in previous auctions is 4075 euros. This suggests that the hammer price could be above the starting price, especially given the high condition of the coin.

4. Auction trends: The coin has been auctioned 14 times, with an 85.7% sell-through rate, indicating consistent interest in this coin.

Based on these factors, an estimated maximum purchase price could be in the range of 5000 to 7000 euros, considering that the condition is FDC and that previous hammer prices for coins in similar conditions have reached those levels.

Therefore, a reasonable maximum purchase price could be between 6000 and 7000 euros.