How to read a colour pie
Every puzzle in The Flag Slice is a pie chart. It looks simple: a few coloured slices, a percentage on each and a legend of colour names. But each of those numbers comes from measuring a real flag, and once you know how the measuring works, the pie tells you far more than it first appears to.
This guide explains where the numbers come from and then walks through a method for reading any pie.
Where the percentages come from
Each flag starts as an image of the official design. The game draws it at 640 pixels wide, in its true proportions, and counts the pixels of every colour. Fine edges are drawn crisply rather than blurred, so a red stripe beside a white one does not produce a band of pink pixels between them.
Real flags are not printed in perfectly flat colours, so the game then groups shades that the eye would call the same colour. Two reds that differ only slightly become one red. The colour you see on each slice is the average of the pixels in that group, so Japan's disc is shown in its own deep red rather than a generic one.
The sixteen colour names
Every slice is given one of sixteen names: White, Black, Grey, Red, Maroon, Pink, Orange, Brown, Yellow, Olive, Green, Teal, Light blue, Blue, Dark blue and Purple. The names are chosen from how light, how vivid and what hue the colour is, not from what a country calls it. That produces a few surprises worth knowing:
- Crimson and orange-red can both read as Red. Latvia's dark crimson is named Red, which is why its pie matches Switzerland's. Bhutan's saffron is also named Red.
- "Gold" is Yellow. Heraldic gold on coats of arms and stars is almost always named Yellow.
- Blue comes in three names. Light blue, Blue and Dark blue are separate slices. France and the United Kingdom use Dark blue; Sweden and Iceland use Blue; Micronesia is Light blue.
- Teal is real. Kazakhstan's sky blue and Cameroon's green both come out as Teal, a useful clue on its own because few flags have it.
Small details and "Other detail"
A colour needs at least 1.5% of the flag to earn its own slice, and a pie shows at most six named colours. Smaller areas of a colour that is already on the pie join that slice. Anything else, such as the fine linework of a coat of arms, goes into a grey slice called Other detail.
Other detail only appears when it reaches 1%. Below that it is dropped and the remaining slices are scaled up to fill the pie. So a large, busy emblem leaves a visible Other detail slice, while a tiny one can disappear completely. Alaska's gold stars are a good example: they are so small that its pie reads as a single slice of Dark blue.
When you see Other detail, think coat of arms, seal or intricate emblem. Brazil, Mexico, Spain, Ecuador and Guatemala are among the countries that show it.
Why thirds read 34, 33, 33
Percentages are rounded to whole numbers, and they always add up to exactly 100. A flag of three equal bands is a third each, which cannot be written in whole numbers, so one slice gets the extra point. Germany shows Black 34, Red 33, Yellow 33. The 34 does not mean black is larger; it is the rounding. Treat any 34/33/33 pie as three equal bands.
The same goes for 50/50 pies, 67/33 pies (Nigeria's green, white, green is Green 67, White 33) and other neat fractions. Neat numbers usually mean simple bands.
A method for any pie
- Count the slices. Two-colour pies narrow the field quickly. Among countries, 39 flags have two colours and only two have six (South Africa and South Sudan).
- Find the biggest slice. If one colour is over about 60%, the flag is probably a plain field with a design on it: a cross, a disc, a star or a canton. Japan is White 81, Red 19; Bangladesh is Green 79, Red 21.
- Look for neat fractions. 50/50, 67/33 and 34/33/33 point to bands. Uneven numbers, like the United States' Red 42, White 39, Dark blue 19, point to more complex designs.
- Read the small slices. A slice of 2–8% is usually a star, a sun, a crescent, a thin border or a fimbriation (the narrow line that separates two colours). China is Red 98, Yellow 2: a red field with small yellow stars.
- Check for Teal, Maroon, Purple or Orange. Rare colours shrink the list dramatically. Fewer than a hundred of the 4,600 flags in the catalogue contain Purple, and the same is true of Teal.
- Use the hints in the right order. If you know the palette but cannot decide between layouts, the layout hint usually settles it. If you can picture several flags with that layout, the clue names the kind of place and the region. Each costs one point.
Practise on these
Try to name each flag before reading the answer:
- Red 62, Dark blue 20, White 18. A red field with a white-edged blue cross. Norway.
- Green 69, Yellow 18, Dark blue 12, Other detail 1. A green field, a yellow shape, a blue globe with a motto. Brazil.
- Black 49, Green 25, Red 25, Other detail 1. A wide black band between red and green. Libya.
- Blue 51, Yellow 49. Two equal bands. Ukraine, though more than twenty other flags share this pie.
The more pies you read, the faster the patterns jump out. Within a few days, a 76/24 red and white pie will look like Denmark before you have consciously done the arithmetic.