Need a pen and paper combat mechanic

Could you make some kind pf physical challenge using the pen and paper? For example, a randomizer "board" of a circle divided into slices, each with its own value. When someone "rolls dice", they hold the pen upright with their finger and the point against the center of the circle, then let go. Whichever slice the pen falls on is the result of the "die roll". Some similar dexterity-based mechanic could replace it.

How about a bloated version of Rock / Paper / Scissors?

Use the color wheel
Red - Purple - Blue - Green - Yellow - Orange (Repeat, Red again, Purple, etc.)

In any combat decide which player is the aggressor and which is the defender. Both secretly pick a color and write it down. They reveal their choices simultaneously.

Colors the same - Aggressor scores a Direct hit! Maximum damage.

One off - Major damage to defender
Examples: Red and Purple, or Blue and Green

Two off - Minor Damage to both Defender and Aggressor
Examples: Red and Blue, or Green and Orange

Opposite colors - Complete miss - No damage to Defender
Examples: Red and Green, Purple and Yellow, or Blue and Orange

Hope this helps,
- KrisW

How about simulating a dogfight by drawing arrows to indicate your plane's facing?

This idea is an offshoot of a blog post I saw a long time ago where players drew left and right arrows on lined A4 paper. Don't remember the rules, exactly, but it's easy enough to make some new ones. :)

Draw an 'nxn' grid (5x5?) and start each player in the middle of opposing edges.

Players draw a dot on the grid to represent position, and an arrow off the grid to represent heading.

Players then secretly draw arrows representing their next maneuver. Players may draw 2 arrows (high speed) or 1 arrow (low speed), and may turn at most 90 degrees if moving fast, or 180 degrees if moving slow.

Players then reveal maneuvers. Fast players move in the direction of their current arrow, then apply their first turn arrow.

Slow players move in the direction of their current arrow, then apply their turn arrow.

Fast players move in the direction of their current arrow, then apply their final turn arrow.

After each move, assess damage as follows:
1) Facing enemy within 'm' (2?) squares: inflict 1 damage
2) Occupy same space as enemy: inflict 2 damage (independent of facing)

First player to inflict 'p' damage (5?) wins.