R&N is a new candy with magical (yet mathematical) properties. Not all candies are the same size. When removing the largest R&N from a new bag, the bag becomes 1/2 full; removing the second largest makes the bg 1/3 full; removing the third largest makes it 1/4 full, and so on. Dr. Lutinski opens a new bag on Monday and eats the largest candy. On Tuesday he eats the next few largest, leaving 5/14 fewer than on Monday. How many did Dr. Lutinski eat?

To solve this problem, we can work backwards and set up equations using the given information.

Let's assume that there are "n" candies in the bag initially.

According to the information given, removing the largest candy leaves the bag 1/2 full. So, the equation for this scenario would be:
n - 1 = (1/2)n

Simplifying the equation, we get:
n - 1 = n/2
2n - 2 = n
n = 2

This means that initially, there were 2 candies in the bag.

Now, let's determine how many candies are left after Dr. Lutinski eats the largest and the next few largest on Tuesday.

On Tuesday, we have (2 - 1) - 5/14 = 1 - 5/14 = 14/14 - 5/14 = 9/14 candies left.

Since there are 9/14 candies left, it means that Dr. Lutinski ate 5/14 of the candies.

To find out how many candies Dr. Lutinski ate, we can multiply 5/14 by the total number of candies initially:
(5/14) * 2 = 5/7

Therefore, Dr. Lutinski ate 5/7 of a candy.

It's important to note that in this scenario, since the candies may have fractional sizes due to the ratio between the remaining candies and the initial number of candies, Dr. Lutinski may have eaten a fraction of a candy.