Use Castle Creek Trailhead.
The Conundrum Couloir is a great snow climb reaching nearly 50 degrees.
Ascend past the Montezuma Mine to the upper bowl directly under Conundrum's North Face. The Couloir is obvious. It is a straightforward snowclimb maxing out around 47 degrees. There may be a problem cornice at the top that is often passed on the right. This couloir tops out right near the summit.
The usual and easiest return is to descend to the Castle - Conundrum saddle and begin a series of glissade/hike cycles back down to the 4x4 trailhead. You won't need your crampons for the hiking parts so stow them securely at the top.
This is a basic snow climb. Ice ax and crampons are required. Helmet is recommended. Rope and pro are optional.