The remainder on a beer mat has to land on somebody

One round beer mat, furred at the edge, one corner gone soft and stained. In biro, a column of four numbers, a ruled line, a total, a division sign, and a circled answer.

40, 40, 35, 25. Ruled line. 140. ÷ 3. 46, circled.

Why are there four numbers if the money's being split three ways?

Because the four numbers aren't three people's shares — they're four separate amounts that got added together before anyone divided anything.

40, 40, 35 and 25 read like they might already be four portions, but a portion doesn't need adding up. These four are contributions collected at different points, or from different sources, across one night — takings that only become one number once they're stacked into a single total. The division only starts after the addition finishes, which is the whole reason the mat needed a ruled line separating the two.

Why is 46 circled when 140 divided by three isn't a whole number?

Because 140 divided by three is 46.67, and somebody rounded down to 46 and circled it anyway.

Three people multiplied by 46 comes to 138, not 140 — two short of the total on the mat. That gap didn't vanish; somebody absorbed it, whether by taking a slightly smaller share themselves, by letting the two go toward a shared cost, or simply by not chasing it. The mat doesn't say which. It just shows the working, including the exact point where a clean division stopped being possible and a decision got made instead.

Why work it out on a beer mat rather than paper?

Because a beer mat is what happens to be within reach at the end of a night, and it's designed to be thrown away.

Nobody plans to keep this sum. It's done fast, standing up, by somebody who's tired, on the nearest absorbent surface — which on a bar is a coaster, not a notebook. The furred edge and the damp stain aren't decoration; they're what a beer mat looks like after it's spent an evening under glasses before it ever got written on.

Do I need permission to print a beer mat design?

No — a plain round mat with hand-written biro on it belongs to nobody.

A specific brewery's printed coaster design is its own property, but a blank mat used as scrap paper is a generic object anybody can draw. Your own four numbers, your own total, your own rounding, is the version that's actually yours — the same way a float counted into a tin before the doors open belongs to whoever counted it.

Does this only apply to splitting a door take three ways?

No — any quick split among an odd number of people, done under time pressure, runs into the same remainder. A takeaway bill among three, fuel money among five, a shared cost among any number that doesn't divide the total cleanly: the mat is one instance of a problem that shows up wherever cash gets pooled and then has to come back apart.

Isn't rounding down by less than one a trivial amount to worry about?

The amount is small. What it decides isn't.

Rounding down means somebody's share is short of an exact third, every time this method gets used. Over one split it's a fraction of a number nobody would notice. Over a run of nights it's a pattern — the same person, or the same rounding rule, quietly taking the loss each time, which is a different thing from a one-off shortfall. What actually happened is easier to see once everything's counted out at the end of the night, not while it's still being worked out under pressure.

Does it print well?

Yes — it's biro on a plain circle, which is about as simple as a print gets.

One ink for the numbers and lines, one flat colour for the mat itself. Bone, cream or another pale warm ground reads convincingly as a coaster, and the furred edge and stain print as soft shapes rather than fine texture — nothing here needs resolution finer than the fabric can hold. A hand-written invoice runs into the same paper-and-pen arithmetic over a single figure, worked out by hand for the same reason.

How do I get one made?

Describe the split at JustOG — the figures, the total, and how the remainder got handled. Pick a direction, drag the crop frame, see it composited on the real garment, and it's made to order and shipped.

Designs other people have published are in the shop.

Someone got 46. Someone else got 46. The third 46 came up two short, and nobody wrote down whose.