3C

3C tools · tier 1: geometry

Place the balls — how to play it

Drag the three balls to exact positions (mm), read distances to rails and between balls, and list every geometric path to score. Built for phones.

123456771, 71213, 7171, 53
Drag with finger or mouse · arrow keys ±1 mm (Shift ±10)
Measurements (mm)
BallTop long railRight short railBottom long railLeft short rail
Cue ball86.2209.949.767.9
Ball 167.967.967.9209.9
Ball 267.9209.967.967.9
PairCentre–centreEdge–edge
Cue – Ball 1143.2137
Cue – Ball 218.312.1
Ball 1 – Ball 2142135.9

Table 2840 × 1420 mm, balls Ø 61.5 mm. Rail distances measured from the ball edge.

Paths to score 42

Paths built by mirror reflection, sorted by length (shorter is usually easier). No english, speed or friction yet — tier 2 adds physics, tier 3 adds make probability.

How to use

  1. Drag the cue ball (white), ball 1 (yellow) and ball 2 (red) to their real positions. Coordinates in mm show on each ball.
  2. Read the measurements: distance to each rail, centre–centre and edge–edge; frozen balls are flagged in red.
  3. Pick a path from the list to draw it: “ball 1 first” (cue → ball 1 → ≥ 3 rails → ball 2) or “rail first” (bank).
  4. Tap “Share position” to send the link to a friend or coach — the link holds all three coordinates.