MathDB
Martian, Venusian, and the Human! - [IMO LongList 1971]

Source:

January 1, 2011
combinatorics unsolvedcombinatorics

Problem Statement

One Martian, one Venusian, and one Human reside on Pluton. One day they make the following conversation:
Martian : I have spent 1/121/12 of my life on Pluton. Human : I also have. Venusian : Me too. Martian : But Venusian and I have spend much more time here than you, Human. Human : That is true. However, Venusian and I are of the same age. Venusian : Yes, I have lived 300300 Earth years. Martian : Venusian and I have been on Pluton for the past 1313 years.
It is known that Human and Martian together have lived 104104 Earth years. Find the ages of Martian, Venusian, and Human.*
[hide="*"]*: Note that the numbers in the problem are not necessarily in base 10.10.