The twelve zodiac symbols, and what each one draws

Twelve pictures, not twelve letters

It is easy to treat the zodiac signs as arbitrary marks, the way most people treat the symbols on a keyboard. They are not. Every one is a stylised drawing that has been simplified over roughly two thousand years of copying, and once you know what each is a picture of, the shapes stop being arbitrary and become obvious.

Aries is a pair of ram's horns curling outward from a central line. Taurus is a bull's head with horns above it — a circle with a crescent on top. Gemini is the Roman numeral two, two uprights closed at each end, standing for the twins. Cancer is a pair of crab's claws, or in some readings two curled shapes facing away from each other. Leo is a lion's mane and tail drawn as a loop with a tail curving off it. Virgo is a letterform, an M with a closing loop, from the Greek for maiden.

The second half continues the pattern. Libra is a set of scales: a horizontal bar with a raised centre. Scorpius is a line of humps ending in an arrow, the scorpion's barbed tail. Sagittarius is an arrow on a bowstring, the archer's shot in mid-flight. Capricornus is the sea-goat, a horned head trailing into a fish's tail. Aquarius is two parallel zigzags, water. Pisces is two fishes facing away from each other, joined by a cord.

Why the astronomical names

Two of the twelve appear here under names that may look like typos: Scorpius rather than Scorpio, and Capricornus rather than Capricorn. Both are the constellation names rather than the astrological sign names, and the distinction is real. The constellations are regions of sky with official Latin names fixed by the International Astronomical Union; the signs are twelve equal thirty-degree divisions of the ecliptic that no longer line up with the constellations they were named after, because the Earth's axis has drifted over the intervening centuries.

For a puzzle it makes no practical difference — the glyph is the same either way. It is worth knowing mostly because it explains why you will see both spellings around, and which one belongs to which tradition.

The clearest difficulty experiment on the site

This category is unusual in that every board is exactly the same size. Twelve puzzles, all 15×15, so nothing about the grid varies. What does vary is difficulty, and it splits eight hard to four normal — which means the entire difference comes from the shape of the glyph rather than from the size of the frame. There is no other category on the site where the comparison is this clean.

The four rated normal are Aquarius, Gemini, Sagittarius and Scorpius. Look at what they are made of. Aquarius is two parallel zigzags — long, straight-ish strokes. Gemini is two uprights closed by bars top and bottom, which is very nearly all straight lines. Sagittarius is an arrow: a straight shaft with a crossbar. Scorpius is a run of humps ending in a barb, a long horizontal that stays roughly on one level.

The eight rated hard are Aries, Cancer, Capricornus, Leo, Libra, Pisces, Taurus and Virgo. Ram's horns that curl. A crab's claws that curl. A lion's mane drawn as a closed loop. Two fishes tied together. Every one of them is dominated by curves that close on themselves, and a closed curve rendered in squares becomes a staircase of ones and twos.

Why curves are hard and straight strokes are easy

The mechanism is worth spelling out, because it generalises well beyond this category. A clue of length k in a line of n cells forces 2k − n cells to be filled. On a fifteen-cell line, a clue of 12 hands you nine cells immediately; a clue of 3 hands you nothing at all.

A long straight stroke produces exactly the first kind of clue. Gemini's uprights run most of the height of the grid, so their column clues are large numbers and the board opens up on the first pass. A curve produces the second kind: as a circle or a hook crosses a line it contributes a run of one or two cells, sometimes two separate short runs on the same line, and none of them force anything on their own. Every cell has to come from the interaction of a row clue with a column clue instead.

So the practical order through this category is not random even though all twelve boards look alike in a listing. Start with Gemini or Aquarius, which are close to solvable line by line. Move on to Sagittarius and Scorpius. Leave the curled glyphs until last, and expect them to take roughly twice as long — not because they are bigger, since nothing here is bigger, but because the outline gives you nothing for free.

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