Elliot gets it in one.

Well here is my submission:

The Die TenTwentySix System:

Each Character has 3 abilities: Physical, Social and Mental
Assign one of these dice to each ability: d6, d10, d20

Each character has Hit Points equal to the maximum value of their physical die.
Each character has Sanity Points equal to the maximum value of their Mental die
Each character has Ego Points equal to the maximum value of their Social die

When two people enter a contest, the most relevant ability is chosen for both participants and they each roll their corresponding die. All dice are "exploding" and the highest roll wins. A tie means that no decisive victory was made this turn unless another character jumps in to help one of the participants.

Aiding another character adds +2 to their roll if you make the same roll and are no more than 2 points below their roll.

Combat: Combat is an opposed Physical roll. If the attacker wins, then their opponent suffers damage equal to the amount by which the attacker’s roll beat the defender’s roll.

Magic: Magic is resolved by an opposed Mental roll. If the attacker wins, they may determine some effect that the defender suffers (sees an illusion, is charmed etc.). Magic can cause the defender to loose hit points or sanity points equal to the amount by which the attacker’s roll beat the defender’s roll.

Social Influence: You can make opposed Social rolls to convince someone to listen to you, and another to convince someone to help you. If they are hostile you must first make a social roll to keep them from attacking you. You can also engage in social combat by debating and flinging insults. Social combat is resolved like physical combat except it is based off of the Social statistic.

Damage: When a character is below half their hit points they suffer -1 to all Physical die rolls. When they are at 0 hit points they are unconscious. They are dead at -5.

When a character is below half their sanity points they suffer -1 to all Mental die rolls. When they are at 0 hit points they are temporarily insane. They are permanently insane at -5.

When a character is below half their Ego points they suffer -1 to all Social die rolls. When they are at 0 Ego points they are dishonored and outcast. They become game designers at -5.

Exploding Dice: On any die roll, if you roll the maximum value on your die you can roll again and add the result to your original roll.

Note: I realize that this game is far from "ballanced," and would pobably work better with a d8 a d10 and a d12 instead of a d6 a d10 and a d20, but those were the dice I had to work with.