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Balance Loop

One loop. Measure every circle’s arms.

Balance LoopPuzzle, Logic, Casual

Hall of records

Balance Loop

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How to play

Goal
Draw one non-crossing loop through every circle, with equal arms at white circles, unequal arms at black circles, and any number equal to the two arm lengths added together.
How it ends
A chart finishes when the single loop and every circle agree; Undo and Erase repair mistakes, so there is no loss state.
Record
The fastest uninterrupted first solve of each chart is kept with its holder's name; replay is practice.
Worked visual example for Balance Loop
Worked example. See the rule happen, then follow the numbered rules below.
  1. Draw one closed, non-crossing loop with horizontal and vertical links between neighbouring centres. Visit every circle; blank centres are optional. No branches or separate loops.
  2. At each circle, measure both arms until their first actual turn. Count links, including the link reaching that turn. Continue through other circles. White arms are equal; black arms differ. A printed number is their sum. Circles may turn or go straight.
  3. Tap an edge to draw. Drag a route, or select neighbouring centres and press Draw. Cross notes are optional; Undo and Erase repair mistakes.
  4. Choose Pan to move a large chart without changing ink, including after completion.
  5. Restart preserves the first clock. Reload preserves marks and Undo; resumed finishes stay local. Replay is practice.

Controls

Mouse / touchTap edges, drag routes, or select neighbouring centres and press Draw
Arrows / Shift + arrowsMove between centres / extend a route
Enter / SpaceSelect a centre
L / C / ELine / Cross note / Erase
PDraw the selected route
PanDrag the view without changing ink
Z / YUndo / Redo
RRestart confirmation
ControllerD-pad moves; A selects; Y draws; X erases; shoulders Undo/Redo; B returns; Start settings.

Tips for Balance Loop

  • Find the actual turn An arm continues through a straight circle; measure until the path really bends.
  • Add both arms White four needs two links in each arm. Black five needs two different lengths adding to five.
  • Keep one loop Closing a small loop early is wrong if another circle remains outside.

Questions about this game

Must every centre be visited?

Only circles must be visited. Blank centres may stay unused.

Must white circles go straight?

No. Either colour may turn or go straight; the rule compares arm lengths.

Does a circle stop an arm?

No. Continue through circles until the first actual turn.

Can replay improve my first time?

No. Your first finish stays unchanged; replay is practice.

All charts are open. Cross notes are optional. Reload retains marks, Undo and the clock; resumed finishes stay local. Practice preserves your first time.

Watch how to play

The rules, then Chart 001 played start to finish. Played by an automated player at a person's pace; the narration is a synthetic voice. English captions.

About Balance Loop

Trace an instrumentmaker’s chart in bronze, ivory and indigo. Every circle belongs to one loop; empty centres may remain unused.

All 160 original charts are open: sixteen at 4×4 and forty-eight each at 5×5, 6×6 and 7×7. Each has one independently verified ending and a complete deduction path.

An uninterrupted verified first solve can claim the named fastest time. Replay preserves your first finish.

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