Cipher methods Numerals

Mayan numerals

Vigesimal (base-20) numeral system invented by the Maya, using only three symbols: the dot (1), the bar (5) and the shell (0). One of the earliest systems in history to feature a positional zero.

Family :: Numerals
Difficulty :: Beginner
Era :: 4th century CE, Maya civilisation (Mesoamerica)

Also known as : Maya numerals · Mayan base-20 · dot-bar-shell numerals

Mayan numerals are one of the oldest documented base-20 (vigesimal) numeral systems, used by the Maya civilisation of Mesoamerica from the 4th century CE. Their historical significance comes from two innovations:

The use of a positional zero as early as the 4th century — almost simultaneously with India, and centuries before zero spread to Europe via Hindu-Arabic numerals.
A minimalist graphic vocabulary of only three primitives: the dot, the bar, the shell. It is one of the most economical systems ever designed.

Principle

The three primitives

•   (a dot)         =  1
———  (a bar)         =  5
🜎   (a shell)       =  0

Any value from 0 to 19 is composed by stacking dots and bars in a single cell, read from bottom to top:

Value 0  : 🜎             Value 10 : ━━     (two bars)
Value 1  : •              Value 11 : •━━
Value 2  : ••             Value 12 : ••━━
Value 3  : •••            Value 13 : •••━━
Value 4  : ••••           Value 14 : ••••━━
Value 5  : ━━ (one bar)   Value 15 : ━━━ (three bars)
Value 6  : •━━            Value 16 : •━━━
Value 7  : ••━━           Value 17 : ••━━━
Value 8  : •••━━          Value 18 : •••━━━
Value 9  : ••••━━         Value 19 : ••••━━━

Vigesimal positional notation

Numbers ≥ 20 are written vertically, units (20⁰) at the bottom, higher powers (20¹, 20², …) above:

        ━━━ (3 × 400 = 1200)
        🜎  (0 × 20 = 0)
        ━━ (2 × 1 = 2)
        Total: 1202

This system allowed the Maya to record astronomical dates, calendrical cycles (the famous Long Count ending on 21 December 2012) and stellar positions in remarkable compactness.

Why base 20?

Choosing base 20 is common to civilisations that count fingers + toes. The same choice appears in the Aztec, Yoruba and Inuit (Kaktovik) systems, and — residually — in French: quatre-vingts literally means “four twenties” (4 × 20 = 80).

The advantage over base 10: each glyph stays under a score — a number like 1949 (4 base-10 digits) fits in 3 cells in base 20 (4 · 20² + 17 · 20 + 9 = 4 · 400 + 17 · 20 + 9).

As a cryptographic device

Mayan numerals are not a cipher in the strict sense — the table has been documented since colonial codices (16th century). But they pair beautifully with rank-based alphabet substitution:

Apply A1Z26 to the plaintext: CIPHE → 03 09 16 08 05.
Turn each number into a Mayan glyph: CIPHE → 5 drawings of dots and bars.

The visual effect is instantly evocative of pre-Hispanic inscription. A perfect fit for a puzzle themed around pre-Columbian civilisations or an Indiana Jones-style escape room.

Comparison with other numeral systems

System	Base	Primitive symbols	Positional zero	Compactness
Roman	10	7 (I V X L C D M)	No	Low
Mayan	20	3 (• ━ 🜎)	Yes	Very good
Babylonian	60	2 (nail, hook)	Late	Good
Hindu-Arabic	10	10 (0 through 9)	Yes	Good
Cistercian	10	Combinatorial	No	Excellent (1 glyph)

The Mayan system stands out for its high base + early zero + minimalist graphics — a rare combination in numeral history.

Legacy and rediscovery

16th century — Spanish missionaries (Bartolomé de las Casas, Diego de Landa) partially documented the system, often misinterpreting it.
19th century — gradual decipherment by Ernst Förstemann (1893) on the Dresden Codex.
20th century — full recognition as a sophisticated numeral system, studied in archaeomathematics programmes.
2012 — wave of popular interest around the “end of the Long Count” (a calendar reset, not an apocalyptic prophecy).