To determine which set contains the 5kg balls using a digital weighing machine just once, take a different number of balls from each set. For example, take 1 ball from the first set, 2 from the second, 3 from the third, and so on, up to 10 balls from the tenth set. Weigh the total number of balls together. If all balls were 10kg, the total weight would be 550kg (10kg multiplied by the sum of the first 10 natural numbers). If the weight is less than 550kg, the difference in weight will indicate which set contains the 5kg balls, as each 5kg ball will reduce the total weight by 5kg for each ball taken from the respective set. This approach effectively identifies the set with the lighter balls in a single weighing.
