Base 6 (Score 1)

If you count in base 6, you can easily count to 35 on your hands (easily meaning without making strange had positions like every other finger out that binary counting on your fingers would require).
0 - closed hand, 1 - one finger out, 2 - two fingers out, etc.
You use one hand for the ones place, and the other hand is the sixes place.
Using your feet as well allows you to count to 1295!