The wager the brothers lost carried precise terms, and the whole middle of the epic is the working out of them. Twelve years in the forest, then a thirteenth lived in disguise; if they were recognised during the thirteenth, the twelve years began again. The Kauravas therefore had a strong interest in finding them, and the search runs underneath the forest books.
The thirteenth year is spent at the court of Virata in Matsya, and it nearly fails at the end. Bhima kills Kichaka, the queen's brother, for pursuing Draupadi, and the manner of the killing tells anyone who thinks about it that a Pandava is in the palace. A cattle raid follows, Arjuna takes up his bow to defend the herds, and he is seen.
Duryodhana then makes a calendrical argument: the year is not complete, the disguise was broken early, and the exile restarts. Bhishma answers him with the reckoning. The lunar year runs short of the solar one, the shortfall is made up by intercalary months, and counted properly the thirteen years were finished before Arjuna was recognised. Duryodhana does not accept the ruling and refuses the kingdom anyway, which removes the last legal obstacle to war.
It is a striking passage to find in an epic. The claim to a kingdom, the deaths of millions and the argument of the entire poem hinge, for one scene, on how a calendar reconciles months to the sun, and the grandsire of the family settles it as a technical question.