Like many generals, Darius III had initially underestimated his enemy. Therefore, he hastily gathered war elephants, 200 chariots, infantry and cavalry and recklessly rushed into battle. The Macedonians immediately captured the elephants, and Alexander’s 7,000 horsemen and 40,000 infantry put the Persians to flight.

Indeed, some historians claim that Darius’s army outnumbered the Macedonians by ten to one. However, there are more conservative estimates. How many horses took part in the battle if a chariot was harnessed with two 2 horses, and Darius had 8 thousand more cavalry than Alexander had infantry? Remember that this event took place on October 1, 331 BC, after which the Achaemenid Empire ceased to exist.¹⁶

G.5. Calendars and sport

As you may have already guessed, we are talking about the Olympics. From the first Olympics the ancient Greeks began to count years using their calendar. Calculate in what year, according to the ancient Greek calendar, this book was published, if the first Olympics took place in 776 BC.

G.6. The Battle of Thermopylae

The Battle of Thermopylae took place in September 480 BC. This unique battle is notable for an almost 40-fold superiority of the Persian forces. If the Greeks had 200 soldiers less, then, according to Herodotus¹⁷, the Persian army would have been 40 times larger than the Greek. As you know, the Spartans, like the rest of the Greeks, fought to the death. Only the betrayal of a local resident allowed the Persians to attack the rear of the Greek positions. Leonidas foresaw this and therefore sent part of his army back. After 4,000 Greeks were killed and the Persians lost 20,000, the Persian army became 150 times larger than the Greek. How many soldiers were in the Persian army?

G.7. Pericles¹⁸, the father of Athenian democracy, or what did Pythagoras have to do with him?

In history, it is crucial to what came first: Ancient Rome or the Republic of Venice, Caesar or Dmitry Donskoy? After that, there should no confusion about who was born first: Archimedes, Pythagoras or Pericles. All three of them were Greeks and prominent personalities. Pythagoras was born first in 570 BC. He lived 5 years longer than Archimedes. Archimedes lived 10 years longer than Pericles. If we add up all the years they lived, we get 220 years. Pericles was born 4 years after the death of Pythagoras. How many years passed between Pericles’ death and Archimedes’ birth, if 358 years passed between the birth of Pythagoras and the death of Archimedes?

G.8. The Peloponnesian War or Sparta versus Athens

As usual, the Peloponnesian War started because Athens wanted the Spartans to be just like them, and the Spartans wanted the opposite. The war lasted from 431 to 404. BC. Historians distinguish two periods of the war: the Archidamian War and the Deceleian War. Between them, there was the «Peace of Nicias» that lasted for six years. How long did the Archidamian War last, if it was a year longer than the Deceleian War did?

G.9. The Parthenon as tremendous historical legacy

Dedicated to Athena, the Parthenon’s construction on the Acropolis¹⁹ lasted from 447 to 438 BC. Even though it was burned down and partially destroyed, it draws attention with its columns’ straight lines. To achieve this, ancient architects curved the straight lines and even tilted some of the columns around the temple’s perimeter. There are 9 more columns on the east side than on the south. In total, there are 16 columns on the south and north sides. How many columns are there along the temple’s perimeter?

G.10. The Battle of Marathon or how the Marathon races were born

On September 12, 490 BC, not far from Athens (42 km), a battle between the Persians and the Greeks took place. This was the first significant victory of the Greeks over the Achaemenid Empire. The Persian forces were 160% larger than the Greek army. The Athenians made up 90% of the Greek army. The Greeks won, and a messenger ran from Marathon to Athens. Upon his arrival in Athens, he fell dead in the square with the words, «Rejoice, Athenians, we have won!»²⁰ After his epic run, the distance he ran (42 km) became known as the «Marathon».

How many Athenians were in the Greek army, if, in total, 36 thousand soldiers took part in the battle?

G.11. A little about Theseus²¹, Aegeus and the Minotaur²²

Having defeated the Minotaur, Theseus, as depicted in the famous myth and cartoon, went home to Athens. Today, in Crete, a ferry from Heraklion, near the Palace of Knossos, runs to Athens in the evening at 21:00. It arrives at 6:00. Could Aegeus have seen the black sail of Theseus’ ship if Theseus sailed at the same time as the modern ferry? Theseus’ ship moved 6 times slower. The distance to Athens is 306 km.

Ancient Rome

We could talk for hours about ancient Rome, and even today, many scholars still study the great history of the Roman Empire. We won’t go deeply into the details here. Instead, we’ll look at some tasks and think about the Empire’s main historical events.

THE FIRST PUNIC WAR

The «First Punic War» is the war between Carthage and the Roman Republic. It started in 264 BC and lasted for 23 years ending with the victory of the Romans.

R.1. Legions are longing for the sea

At the start of the First Punic War, Carthage reigned supreme as the dominant maritime power, and Roman light ships couldn’t inflict any significant damage to the Carthaginian quinqueremes²³. However, by an accident of fate, one quinquereme was thrown on land. The delighted Romans took the ship and carefully disassembled the vessel. They copied the design and constructed a mighty Roman fleet of 100 quinqueremes and 20 triremes²⁴.

How many: legions²⁵, maniples, centurias the new fleet could carry?

R.2. Rowing is an honorable occupation

In the era of the Roman Republic, rowers were highly respected. After the Roman fleet was built, rowers hired and trained tirelessly. How many rowers enrolled in the fleet? The size of the fleet is mentioned in the previous task.

R.3. Toward each other

The distance between Carthage and Sicily²⁶ was 213 km. The First Punic War was still going on, and a fast quinquereme sailed from Lilibey to Carthage with an urgent message. Meanwhile, a small fleet of various ships with reinforcements and provisions set sail for Sicily. How long will it take for the fast ship to meet the fleet if the fleet’s speed is 4 knots and the quinqireme’s is 6 knots? Sailors measure everything in miles. One mile is 1853 m, and a knot – measure of speed, – equals 1 mile per hour.

R.4. How many ships did disappear and where did they go?

In ancient times they went, as a rule, to the seabed. There were several reasons why they sank. Firstly, they could have been damaged in battle, or, simply because of their poor state due to the crew’s negligence, could start leaking. However, the primary reason for ships’ disappearance was Neptune’s²⁷ wrath or forces of nature, to put it in contemporary terms.

1,200 ships of the First Punic War didn’t escape this fate. Carthage lost five out of every twelve ships, while the Romans lost seven of every twelve. In total, who lost more ships and by how many?

The task can be dealt with in two ways, and, of course, we might try to assess whether there were many ships in the ancient fleet compared to modern times.

THE SECOND PUNIC WAR

The Second Punic War lasted since 218 to 201 BC in Italy, Spain and modern Tunisia. Many historians described the war, and many battles were included into military texts and may fascinate even today. For example, the eminent Roman historian Titus Livius²⁸ wrote a book about it called The War with Hannibal. 2,000 years ago.

R.5. The trophies of Saguntum²⁹

The Second Punic war began in 219 BC when Hannibal³⁰ sieged Saguntum. His victorious army captured 2,925 pounds of silver.

Hannibal’s army consisted of Nubian horsemen, Spanish infantry, Carthaginian warriors, tribes from southern Spain, and Balearic slingers³¹. The ratio of their numbers in the army was 1:2 2:1:0.5.

Hannibal made a just decision to divide everything equally between the soldiers. There were 1,000 Balearic slingers in the army. How many asses (ancient Roman currency) did each soldier get? One denarius was worth 10 asses, and one pound is 72 denarii.

R.6. Swift Carthaginian spy

The Roman consul decided to send several triremes to support the armies fighting in Spain, near Massalia, (modern Marseille in France). The fleet was not far from Pompeii³², and Gannon, a cunning Carthaginian spy, found out about this. To warn Hannibal’s army, he would need to travel faster than the Roman triremes. How quickly does Gannon need to travel by land if the distance between Pompeii and Massalia is 791 km by sea? By land, the spy needs to pass through Rome and Genoa. The distance between Pompeii and Rome is 173 km, from Rome to Genoa – 403 km, and from Genoa to Massalia – 346. The average speed of trireme is 5 km per hour. Well, one cannot always have a tailwind! The spy needs to sleep at least 6 hours a day. Otherwise, he might lose his vigilance and get captured by the valiant Praetorians³³.

R.7. The first battle of the Second Punic War

In November 218 BC, Hannibal’s troops approached the Ticinus River. Simultaneously, from Italy, Scipio’s³⁴ troops approached the same river. The first battle took place near this place. From Carthage’s side, only its cavalry took part in the battle. However, the Romans used both cavalry and light infantry, velites³⁵. Hannibal had 6,000 cavalry units. From the Roman side, the cavalry was 100 units more than half of the Carthaginian forces. Moreover, the infantry was 20% more than Hannibal’s cavalry. In total, how many soldiers took part in the battle?

R.8. The Battle of Trebbia or how to win allies