How many boiled eggs can I safely consume a day without added risk of high cholesterol?  

Once or twice a week. An egg a couple of times a week is just fine and should not increase your risk of high cholesterol, as long as you do not have an underlying disease that increases your cholesterol. You can make them even better by removing 1/2 or even all of the egg yolk from the boiled eggs...
2 per week. In general, most people should get 2 egg yolks per week - whites are essentially unlimited.
Eggs. Depends on the person. If the person is healthy and does not have any illness then 2 or 3 eggs aday can be very beneficial. Eggs are a good source of protein and of beneficial fats and carbohydrate. Remember that an egg contains everything necessary to give life to a chick.