Semper tres

I'm translating a piece about Gauguin, the painter, and it is said about him "I believe I learnt, during my childhood and in that seminary, to hate hypocrisy, double dealing and sneaking *(semper tres)*, and to distrust anything that ran contrary to my instinct, heart and reason. Gauguin says these words about his school days in a religous school in France.
*semper tres* it is part of a sentence: Non quam duo, semper tres
and it means: never go in twos - always in threes.
this is a rule they had to keep at school. I wanted to know the origin of it, what was really the reason for this rule, to be able to understand the connection to this paragraph.
and my thanks to everyone who tries to enlighten me.
Miri

This'll be of no help, but it used to be claimed that in the days of the Cold War, the KGB used to only go around in threes - why? One who could read, one who could write, and the last to keep a watchful eye on the intelligentsia.

The article linked below suggests that the purpose of the rule in seminaries was to prevent sexual activity between students.
[Dead link removed]