Beautiful Liars
Number Theory
Level
4
Louis gives one number of three digits \(\overline{abc}\), to their students. They had the following conversation:
\(\text{Alan}:27\) divides \(\overline{abc}\)
\(\text{Blas}:11\) divides \(\overline{abc}\)
\(\text{David}:a+b+c=15\)
\(\text{Jane}:\overline{abc}\) is a divisor of \(648,000\)
\(\text{Ronnie}:\overline{abc}\) is a perfect square
Only three of this students told the truth. Find \(\overline{abc}\).
by
Paola Ramírez