Ephesus restored to its original appearance by artist Ádám Németh**The Palatine Anthology** is a 10th century CE Byzantine anthology of earlier works by Meleager, Philippus and
Agathias, including curiously a set of number puzzles in Book XIV. The codex was put together by Constantine Cephalas of Rhodes
and the only known copy is held at the Palatine Library in Heidelburg, Germany. These examples were published
with translations in *Greek Anthology Volume 5* in 1918 by William Roger Paton. He says the puzzles are in the style
of Metrodorus, a Greek grammarian and mathematician who lived in the 6th Century CE. For anyone who has done mathematics
at school these are all easy puzzles to solve.

1 (epigram 1)

Polycrates speaks: Blessed Pythagoras, Heliconian scion of the Muses, answer my question: How many in thy house are
engaged in the contest for wisdom performing excellently?

Pythagoras answers: I will tell thee then, Polycrates. Half of them are occupied with ‘belles lettres’, a
quarter apply themselves to studying immortal nature; a seventh are all intent on silence and the eternal discourse of their hearts.
There are also three women, and above the rest is Theano. That is the number of interpreters of the Muses I gather
round me.

2 (epigram 126)

An epitaph for the mathematician Diophantus.

‘Here lies Diophantus,’ the wonder behold. Through art algebraic, the stone tells how old: ‘God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father’s age—chill fate took him. After consoling his fate by the science of numbers for four more years, he reached his end.’How old was he when he died?

3 (epigram 127) Demochares lived a quarter of his life as a boy, a fifth part as a youth, a third as a man, and when he reached grey old age he lived thirteen years more. How old was he when he died?

4 (epigram 135) We three Loves stand here pouring out water for the bath, sending streams into the fair flowing tank. I on the right, from my long-winged feet, fill it full in the sixth part of a day; I on the left, from my jar, fill it in four hours; and I in the middle, from my bow, in just half a day. Tell me in what a short time we should fill it, pouring water from wings, bow, and jar all at once. [Note: A day was measured as 12 hours]

5 (epigram 137)
Let fall a tear as you pass by for we are those guests of Antiochus whom his house killed when it fell;
and God give us in equal shares this place for a banquet and a tomb. Four of us from Tegea lie here, twelve from Messine,
five from Argos, and half of the banqueters were from Sparta, and Antiochus himself. A fifth of a fifth part of those
who died were from Athens and do thou, Corinth, weep for Hylas alone.

How many people died in the accident?

1 Pythagoras has 28 students not counting Theano. (14+7+4+3)

2 Diophantus was 84 when he died. Diophantus’s life X years = Boyhood X/6 + Youth X/12 + Before Marriage X/7 + 5 +
Son’s life x/2 + 4.

We know that Diophantus’s age when he died is a multiple of 6, because his boyhood lasts exactly one-sixth of that age.
Not only is it a multiple of 6, but also 12, 7, and 2. There’s an infinite set of values that are multiples of those
four numbers, but reality tells us that there’s only a small window of potential ages that Diophantus might have reached.
The least common multiple of 6, 12, 7, and 2 is 84. The next potential multiple of these numbers is 168 – well beyond
human lifespan in ancient Greece!

3 Demochares lived to 60 years old

4 It will be full in ** ^{1}⁄_{11}** of a day

Say the tank holds 144 gallons; the wings alone flow at 72 gallons per hour, the jar alone at 36 and the bow at 24. So in one hour the combined flow will be 132 gallons. Another 12 gallons are needed which would take another

5 There were 50 people died that day.

*At October 2023 the book is online at https://archive.org/details/greekanthology0005unse/mode/2up*