There are six boxes containing 5, 7, 14, 16, 18, 29 balls of either red or blue in colour. Some boxes contain only red balls and others contain only blue.
One sales man sold one box out of them and then he says, "I have the same number of red and blue balls left over."
Which box is sold out?
(In reply to
Puzzle Answer by K Sengupta)
The six boxes contain a total of 29+18+16+14+7+5=89, which is a odd number.
Now, after selling a particular box, the respective numbers of red and blue balls are equal. Accordingly, it follows that the box sold must contain an odd number of balls.
Thus, the sold out box (- {5,7,29}.
After performing trial and error with each of the 3 cases, we observe that only 29 conforms to the given conditions, as:
• 89-29=60, and:
• 5+7+18 = 14+16=60/2
Consequently, the salesman must have sold the box containing 29 balls.
Edited on July 22, 2022, 1:35 am
Explanation to Puzzle Answer
