Bisect
Drag across the shape and the cut lands where you let go. The keyboard works too — turn with the left and right arrows, shift with up and down, then press Enter. After the cut you see what share each piece took, and a dotted line showing where that same angle would have been exact. Difficulty changes only the shape: how many corners it has and how jagged it is.
Split the shape into two equal areas with a single line. Drag across it and the cut lands where you let go — no ruler, no guides. The keyboard works too: turn with the left and right arrows, shift with up and down, then press Enter. After the cut you see what each piece took, and a dotted line showing where that same angle would have been exact. There is no time limit. It is tempting to think a line through the centre of mass splits the area evenly, but it does not — in a triangle, a line through the centroid parallel to a side splits it 4 to 5.
The score is the difference between the pieces over the whole
After the cut, both pieces are measured with the shoelace formula and 1 − |a − b| ÷ (a + b) is shown as a percentage. A 48-to-52 split is 96.00%, 45 to 55 is 90.00%, 49.5 to 50.5 is 98.00%. The one-line verdict is "exactly half" at 99.99% and above, "almost exactly half" at 99%, "close" at 95%, "off to one side" at 85%, and "well off to one side" below that. Two decimal places are always shown because those two digits are what the game is played for, and the top threshold sits at 99.99% so that a score reading 100.00% is never called anything but exactly half.
Through the centroid is not a half
This is where most people are caught. In a triangle, a line through the centroid parallel to the base cuts off a similar triangle with ratio 2/3, so the areas are 4/9 to 5/9 — a score of 88.89%. The centroid balances a shape; it does not halve its area. The dotted line that appears after a cut is where your exact angle would have split it evenly, found by sixty rounds of bisection, which against a board 100 across is as good as exact. The angle itself is not corrected.
Dragging, the keyboard, and where the shape sits
Drag and release and the cut runs through those two points, but a drag shorter than 4 counts as aiming and does not cut. On the keyboard the left and right arrows turn by 2 degrees and up and down shift by 1; holding Shift makes both 0.2. Enter or Space cuts. The shape is not centred: its size (68–96% of the 86 available) and position are varied every time — if it were always central, a line straight across the middle would be nearly right and nobody would look at the shape.
Difficulty, records and the daily board
Easy has 3–5 corners and is nearly convex, normal 5–7 with slight dents, hard 7–11 and deeply star-shaped. When a concave shape leaves one side in two pieces, their areas are added. The best score is kept per difficulty in this browser, and the daily board's score is kept apart from it. The daily board is generated from the date, so everyone gets the same shape on the same day; it is always normal difficulty and changes at midnight Korean time. Only the first cut of the day is recorded.
Common questions
QDoesn't a line through the centre of mass split it evenly?
No — this is the trap almost everyone falls into. In a triangle, a line through the centroid parallel to a side cuts off a similar triangle with ratio ⅔, so the areas go as (⅔)² = 4/9 to 5/9. Lines through the centroid *can* bisect the area, but passing through it does not make them do so.
QHow is the score worked out?
The difference between the two pieces, over the whole: 1 − |a−b| ÷ (a+b). An even split is 100%, one piece taking everything is 0%. Dividing by the whole is the point — without it the same skill would score lower whenever a large shape came up.
QHard mode shapes are concave — is the area still right?
Yes. A concave shape can leave one side broken into two pieces, and both are counted. A test pins down a ⌳-shaped board cut so the right side splits into two, and also checks that the two areas still add up to the original.
QWhat is the dotted line?
Where the cut would have been exact at the angle you chose. It does not correct your angle — telling you the best direction as well would leave nothing to work out next time. It is found by bisection over sixty rounds, which against a board 100 across is exact for any purpose here.
QIs there really no time limit?
None. This game measures one thing: how well you judge area by eye. Mixing in hand speed would blur what it measures. Difficulty is limited to the shape itself for the same reason.
QWhere should I look to split it exactly?
At area, not the centroid. A convex shape has exactly one correct cut for each direction, and a thin spike sticking out one side holds little area, so the answer lies closer to the body than the eye suggests. The distance between the dotted line and yours after the cut shows which way you were fooled.
QCan I cut the same shape again?
A cut board is finished; it cannot be cut again and the next shape follows. Only the daily board returns the same shape when reopened the same day, and only the first cut of the day counts. Past days' shapes can be reopened from the results card's links to earlier boards.