Twenty kilograms of cheese are on sale in a grocery store. Several customers are lined up to buy this cheese. After a while, having sold the demanded portion of cheese to the next customer, the salesgirl calculates the average weight of the portions of cheese already sold and declares the number of customers for whom there is exactly enough cheese if each customer will buy a portion of cheese of weight exactly equal to the average weight of the previous purchases. Could it happen that the salesgirl can declare, after each of the first $10$ customers has made their purchase, that there just enough cheese for the next $10$ customers? If so, how much cheese will be left in the store after the first $10$ customers have made their purchases? (The average weight of a series of purchases is the total weight of the cheese sold divided by the number of purchases.)
Problem
Source: ToT - 2001 Spring Junior O-Level #3
Tags: algebra unsolved, algebra
19.08.2011 20:29
I believe that this should be the actual problem: Tournament of Towns problem writers wrote: Twenty kilograms of cheese are on sale in a grocery store. Several customers are lined up to buy this cheese. After a while, having sold the demanded portion of cheese to the next customer, the salesgirl calculates the average weight of the portions of cheese already sold and declares the number of customers for whom there is exactly enough cheese if each customer will buy a portion of cheese of weight exactly equal to the average weight of the previous purchases. Could it happen that the salesgirl can declare every time a customer has made their purchase, that there just enough cheese for the next 10 customers? If so, how much cheese will be left in the store after the first 10 customers have made their purchases? (The average weight of a series of purchases is the total weight of the cheese sold divided by the number of purchases.