The Last Gardener

1. The puzzle

The garden contains four grounded arrangements of green segments—called shrubs here—and a bowl holding n pebbles.

Two players alternate turns. On a turn, a player must make exactly one move:

1. Cut one green segment. Any segments no longer connected to the ground immediately fall away.
2. Remove one or more pebbles from the bowl.

The player who makes the last legal move wins. Find the unique n∈{0,…,63} that makes the complete starting position a second-player win, and identify the decorative shrub.

This is a finite, impartial, normal-play game, so Sprague–Grundy theory applies.