What is Balance Loop?
Balance Loop is a loop puzzle with a single, elegant idea: every circle measures the two straight lines that reach out from it, and asks whether they balance. You draw one closed loop through the centres of the cells, passing through every circle on the board. The loop never crosses or branches, and - unlike Masyu or Shingoki - it is free to go straight through a circle or to turn on it. The colour of the circle says nothing about turning; it only reports whether the two arms come out even.
From any circle, look along the loop in both of its directions and measure each arm - the straight run from the circle to the point where the loop next turns. A white circle is balanced: its two arms are exactly equal. A black circle is unbalanced: its two arms are different lengths. If a circle also carries a number, that number is the sum of the two arm lengths. Put colour and number together and the loop has exactly one place to run.
- Draw a single closed loop through cell centres, passing through every circle.
- The loop never crosses or branches, and may leave cells unused.
- The loop may go straight through a circle or turn on it - either is allowed.
- White circle: the two arms reaching out from it are equal in length.
- Black circle: the two arms are unequal in length.
- A number is the sum of those two arm lengths.
- Exactly one loop satisfies every circle - pure logic, no guessing.
How to play Balance Loop online
Click or tap the gap between two neighbouring cells to lay a piece of the loop, and click it again to remove it. The small dots mark the lattice the loop travels along; the circles are the clues it must collect. Keep connecting segments until they close into one loop that passes through every circle and balances each one - the board congratulates you the moment the last circle is satisfied.
Check marks anything that already breaks a rule - a branch, a white circle whose arms have grown unequal, a number that has been overshot - without giving the route away. Hint removes a stray segment first and only then adds a correct one, Undo steps backwards, Reset clears the board, and Solution lays down the full loop when you would rather study a finished board than fight it.
- Tap between two cells to draw or erase a segment.
- Check highlights rule conflicts; it never spoils the route.
- Hint repairs your loop before it extends it.
- Backspace or Delete erases the segment you placed last.
- New puzzle builds a fresh board for the selected size and difficulty.
Reading the circles: arms and balance
The whole game lives in one measurement, so it pays to make it second nature. Stand on a circle and follow the loop out one side until it turns: that distance, counted in segments, is one arm. Do the same on the other side for the second arm. White says the two arms match; black says they differ. The loop reaching a circle and turning immediately on it gives that side an arm of length one, the shortest possible - and an arm is never zero, because the loop always has to leave the circle in two directions.
Numbers turn the balance into arithmetic. A white circle with a number n has two equal arms that sum to n, so each arm is exactly n/2 - which immediately tells you a white number must be even, and pins both arms to a known length. A black circle with a number n splits it into two unequal parts, each at least one: a black 3 is 1+2, a black 5 might be 1+4 or 2+3, but never the even halves. Small numbers are loud: a white 2 is 1+1 (the loop turns one step away on both sides), and a black 2 is impossible, because 2 cannot split into two different positive arms.
- An arm is the straight run from a circle to the loop's next turn, in segments.
- White circle: the two arms are equal; black circle: they are unequal.
- A number is the sum of the two arms; each arm is at least one.
- A white number must be even - both arms are exactly half of it.
- A black 2 is impossible; a white 2 forces an immediate turn on both sides.
Straight or turning - the colour does not decide
The point that trips up Masyu and Shingoki players is that in Balance Loop the colour never tells you whether the loop turns. A white circle can sit in the middle of a long straight line, with equal runs to the turns at either end - or the loop can turn right on it, sending two equal arms off at a right angle. A black circle is the same: straight through with unequal runs on each side, or turning with unequal arms. Colour constrains the lengths, not the geometry.
That freedom is exactly what makes the deductions interesting. When a circle sits against a wall, count the room: an arm can never cross the border, so a white circle near an edge often cannot afford equal arms in one orientation, which forces the other. A black circle in the very corner of the grid must turn there - both its arms run along the borders - so its number splits into the two border distances, and they must differ. Reading the walls against the colour is where most Balance Loop boards crack open.
- A white or black circle may be passed straight or turned on - both are legal.
- Colour fixes whether the arms are equal, not whether the loop turns.
- An arm can never cross the grid border - count the room before committing.
- A corner circle must turn; its two arms run along the two borders.
- Test each orientation against the walls; often only one can balance.
The quiet rules that close the loop
Between the circles, Balance Loop is governed by the bookkeeping every loop puzzle shares, and most stalled solves are unstuck by it rather than by the clues. Each cell the loop uses has exactly two connections - so the moment a cell has two segments, you may mentally seal the other two sides. A cell with one segment is a live end that must keep growing. And the loop is one loop: if joining two ends would close a small circle while other circles remain uncollected, that join is forbidden, however natural it looks.
The 'every circle' rule has a sharp contrapositive that is easy to miss: if your partial loop ever walls a circle off - leaves it in a pocket the path can no longer enter without crossing itself - something earlier is wrong, even though no individual circle is complaining yet. Glance at the unreached circles every few moves and ask whether the loop can still get there. It is a two-second check that saves entire boards.
- Every used cell has exactly two connections - no branches, no dead ends.
- Two segments at a cell? Mentally seal the other two sides.
- Never close the loop while any circle is still outside it.
- A circle the loop can no longer reach proves an earlier mistake.
- Unused cells are fine; uncollected circles are not.
A modern loop from Prasanna Seshadri
Balance Loop is a young puzzle with a clear author: it was created by the Indian puzzlemaker Prasanna Seshadri and first appeared on The Art of Puzzles in 2015. Unlike the Nikoli loop classics that drifted into the world anonymously over decades, Balance Loop arrived fully formed, with a name and a designer, and it spread through the online and championship puzzle scene because its central idea is so clean and so new.
By Seshadri's own account the genre grew out of an attempt to bring length clues - the kind you see in Cave or Four Winds - into a loop puzzle, and then to fold in a second idea: balance. The white and black circles borrow their look straight from Masyu, the pearl-loop classic, but their meaning is different - here the colours mark equal versus unequal splits rather than straight versus turning. That recombination of old parts into something genuinely new is what earned Balance Loop its place in the loop family.
Balance Loop vs Masyu, Shingoki and Slitherlink
All four are single-loop puzzles, and the closed-loop bookkeeping moves between them, but each reads its circles differently. Masyu gives you white and black pearls with a strict geometry rule: white pearls are passed straight, black pearls are turned on. Shingoki keeps that straight/turn grammar and adds a number measuring the straight arms. Balance Loop borrows Masyu's two-colour look but throws the straight/turn rule away entirely - here the colour only says whether the two arms balance, and the loop is free to do either.
That single change flips how it feels in the hand. Coming from Masyu or Shingoki, the hardest habit to break is assuming a white circle means 'go straight' - in Balance Loop it does not. Slitherlink sits further away, drawing its loop on cell edges and counting used sides instead of measuring arms. If you enjoy Masyu's pearls or Shingoki's measured runs, Balance Loop is the natural next step: the same loop discipline, but with a fresh question - not which way does it turn, but do the two sides come out even.
- Masyu: white pearls go straight, black pearls turn - geometry only, no numbers.
- Shingoki: white straight, black turn, plus a number measuring the arms.
- Balance Loop: colour marks equal vs unequal arms; straight or turning is free.
- Slitherlink: loop on cell edges, clues count used sides of a square.
- Shared core: one closed loop, two connections per cell, no premature closure.
Grid sizes and difficulty levels
The 6x6 boards are the training ground: short arms, circles close together, and a white 2 or a corner black circle practically drawing the loop for you. On 7x7 the runs stretch out, the balance arithmetic starts doing real work, and you will meet boards where the middle stays open until two arms finally have to match. The 8x8 boards are full puzzles - longer arms, more circles working together, and stretches where you must read colour, number and wall in the same breath before a single segment becomes certain.
Difficulty changes how much the circles spell out. Easy boards keep a number on almost every circle, so each arm follows from a short calculation. Medium hides many of the numbers, leaving more of the loop to be pinned by balance alone - equal against unequal. Hard hides more still, so you lean longer on the colours and the walls before the loop takes shape. Whatever you pick, the generator solves every board before serving it and keeps only the ones with a single solution - so a stuck position is never a broken puzzle, only a deduction you have not found yet.
- 6x6 - short arms and close circles for learning the balance.
- 7x7 - longer runs where colour and number start to interact.
- 8x8 - full boards with circles that must be read together.
- Easy keeps most numbers; medium and hard lean on the colours.
- Every puzzle is verified to have exactly one solution.