A new addition to the family

Logic Level 4

One joyous morning, Mrs. Tan gave birth to her fifth child, Eric, in Singapore General Hospital. Later in the day, the family of seven bumped into her old friend who was surprised to see a newborn baby. The friend asked how old her four older children were.

Mr. Tan said, "The sum of the ages of our four older children is \(x\) (an integer less than 25). The product is 216."

The friend said, "This isn't helpful. Tell me more."

Mr. Tan replied, "Our oldest child's name is Charles."

The friend said, "Still not enough information."

Mr. Tan answered, "Including Eric, our only daughter, Brenda, is now our middle child."

Mrs. Tan's friend answered, "Aha! Now I know the answer!"

Assuming Mrs. Tan's friend is perfectly​ logical, how old are the four older children? Give your answer as the concatenation of the four ages in descending order. For example, if the four older children are 1, 2, 3 and 4 years old, your answer is 4321.

Note: Mrs. Tan's friend knows what is \(x\) but we as the readers do not.


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