Propositiones ad Acuendos Juvenes/Problems/45 - De Columba

by : Problem $45$

 * De Columba: A Pigeon
 * A pigeon sitting in a tree saw others flying, and said to them:
 * "I wish there were others with you --
 * the same number again and a third time.
 * Then with one of me, there would be $100$."


 * How many pigeons were there at first?

Solution

 * $33$

Proof
Let $x$ years be the number of pigeons there at first.

Then we have: