Olympiad Banks · EisatoponAI

86,000+ free olympiad problems: maths, physics, chemistry, informatics, biology, astronomy. Past papers in English with LaTeX. No sign-up, no ads.

[Olympiad Banks · EisatoponAI @OlympiadBank]

86,000+ olympiad problems in six free banks 🧮⚛️🧪💻🧬🔭
Maths, physics, chemistry, informatics, biology and astronomy, in English with LaTeX.
No sign-up, no ads, updated daily. Links below 👇

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/OlLggGUM2W
The strings fall silent; their hands meet.

In Max Volkhart’s “The End of the Song,” the conversation seems to be just beginning.

#ArtHistory #Painting #eisatopon

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/8tL20CpCma
🔢 A remarkable theorem from 1862!

For every prime p ≥ 5, the numerator of

1 + 1/2 + ··· + 1/(p−1)

is divisible by p².

The hidden power of primes!

#eisatopon #NumberTheory #Mathematics

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/TvSaWd46Z1
🐘 More than a touching moment.

Animals deserve not only our kindness, but our respect, protection, and the freedom to live with dignity.

The way we treat them says much about our humanity.

#eisatopon #AnimalWelfare #RespectForLife

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/vBeQdIOHrs
🎯 Two players start at 0 and take turns adding a number from 1 to 9.

The first to reach a three-digit number wins.

Who has a guaranteed winning strategy?

#eisatopon #MathPuzzle #GameTheory

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/yBGagG76Sm
🔢 72 and 99 give 27.
27 and 45 give 18.
The pattern continues… but the final 7 is NOT a mistake!

Can you find x?

#eisatopon #MathPuzzle #BrainTeaser

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/A7PmSEfLYr
🔢 A prime with 6,400 digits: 6,399 nines and just ONE eight!

Harvey Dubner discovered it in 1991.

10⁶⁴⁰⁰ − 10⁶³⁵² − 1

#eisatopon #PrimeNumbers #NumberTheory

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/BmP6wtNVa5
♟️ One grain of rice on the first chessboard square. Double it on each next square.

Total: 18,446,744,073,709,551,615 grains!

The final square alone has ONE grain more than the previous 63 combined.

#eisatopon #Mathematics #ExponentialGrowth

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/dcn46M6d0Q
📐 Five regular pentagons. Four are congruent.

Can you find the area ratio of one small pentagon to the large one?

#eisatopon #Geometry #MathChallenge

[Olympiad Banks · EisatoponAI @OlympiadBank]

@Olivia_Roseqr https://t.co/xpXS8yYbAP

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/7SDfRJRhOy
Einstein is thinking… What’s your final answer? 🧠

2³ + 3² × 2 = ?

A: 34 | B: 26 | C: 50 | D: 100
#MathQuiz #eisatopon

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/7SDfRJRhOy
Einstein is thinking… What’s your final answer? 🧠

2³ + 3² × 2 = ?

A: 34 | B: 26 | C: 50 | D: 100
#MathQuiz #eisatopon

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/tojAky7aIL
🔢 The Basel Problem puzzled mathematicians for 90 years!

In 1734, Euler discovered:

1 + 1/4 + 1/9 + 1/16 + ··· = π²/6

An astonishing connection between infinity and π!

#eisatopon #MathHistory #Mathematics

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/Hh8GtdzqGH
🔢 8 = 2³ and 9 = 3².

They are the ONLY consecutive perfect powers greater than 1!

Conjectured by Catalan in 1844, proved by Mihăilescu in 2002.

#eisatopon #NumberTheory #Mathematics

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/3qyA6etTf9
🌕How large are the major moons of Jupiter and Saturn?

A beautiful size comparison with Earth as reference shows just how impressive Ganymede, Titan, Callisto and the others really are.

#eisatopon #Astronomy #SpaceScience

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/ef41AsQGog
📄 Why is A4 paper exactly 210 × 297 mm?

The secret is √2!

Halve an A-series sheet, and the new rectangle keeps the same proportions.

A beautiful piece of mathematics hiding in everyday life!

#eisatopon #Geometry #Mathematics

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/rSuVIsdy15
🔢 Is it a coincidence that PRIME adds up to a prime?

P=16, R=18, I=9, M=13, E=5

16+18+9+13+5 = 61

And 61 is prime!

#eisatopon #PrimeNumbers #MathFun

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/RCIRPqLYWu
🎲 Kiyosi Itô died on November 10, 2008.

His stochastic calculus revealed a remarkable rule:

d(Bₜ²) = 2Bₜ dBₜ + dt

That extra dt changed how we model randomness.

#eisatopon #Mathematics #Probability

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/3df9VDr5ko
🌐 You can't comb a hairy sphere perfectly flat!

Every continuous tangent vector field on a sphere must vanish somewhere.

But on a torus? No zero is required.

Topology makes the difference!

#eisatopon #Topology #Mathematics

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/ylk6d3l7AR
🌀 A surface can curve everywhere and still have zero mean curvature!

Enneper's surface (1864) even intersects itself as it extends.

Minimal does NOT mean flat.

#eisatopon #Geometry #Mathematics

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/ftq79Y9t3e
📚 During a job interview, Olga Taussky was asked an inappropriate question about her joint research papers.

G. H. Hardy interrupted:

"That is a most improper question. Do not answer it!"

#eisatopon #MathHistory #WomenInMath

[Olympiad Banks · EisatoponAI @OlympiadBank]

https://t.co/EU9uyh2Yem
🔢 Mathematics once had a 16-letter word for x⁸:

ZENZIZENZIZENZIC!

Robert Recorde used the 17-letter spelling "zenzizenzizenzike" in 1557.

#eisatopon #MathHistory #Mathematics