A barrel is initially filled with pure single malt whiskey. A distiller follows a process to infuse another type of whiskey by removing 10% of the barrel's contents and replacing it with blended malt whiskey. The distiller plans to sell the whiskey once the percentage of single malt drops below 65%. Determine the minimum number of times this operation must be performed.

Let's say the contents of the barrel is X litres, and 10% is being taken out and being replaced every operation,
That means there's 90% of the barrel's contents intact after every operation. 

So, if we start off with X litres of single malt whiskey, after the first operation we will have 0.9X of single malt whiskey,
And after n operations the contents of single malt whiskey will be $$0.9^nX$$

And we want this value to be lesser than 0.65X

After 4 operations the content will be 0.6561X

So, a minimum of 5 operations must be performed