Each of the triangular numbers that are below 1000 is written on a separate card. Some of these cards are then placed in a circle so that, viewed from the center, the right-hand digit of each card matches the left-hand digit of the card to its right. No tricks are used such as turning a card upside-down.

What's the maximum number of digits that can appear on such a subset of the cards?

The required maximum number of digits is 30. This can occur on a subset of 12 cards.