Easy math trivia: numbers and number sense
This first round is the warm-up: place value, Roman numerals, the three properties of addition that every school course covers, and a pair of questions on factors and multiples. Nothing here needs working out on paper, and most of it is recall rather than calculation.
If you are reading these aloud, the three property questions work well together — say the equation, then ask for the name. People who have not seen the words commutative, associative and identity since school usually recognise the rules instantly but grab for the wrong label.
Q1.In the number 534,267,984, what is the value of the digit 8?Tap to reveal
Answer: 80, because the 8 sits in the tens place
Place value multiplies by ten with every step to the left, so the same digit 8 would be worth 800 one column further over and 8 in the last column.
Q2.Which letter is the Roman numeral for 1,000?Tap to reveal
Answer: M
Roman numerals use only seven letters — I, V, X, L, C, D and M — and there is no Roman numeral for zero at all.
Q3.What number does the Roman numeral XL stand for?Tap to reveal
Answer: 40
A smaller symbol placed before a larger one gets subtracted, so XL is 50 minus 10. Put the same two letters the other way round and LX means 50 plus 10, or 60.
Q4.Which property of addition says that 678 + 45 = 45 + 678?Tap to reveal
Answer: The commutative property
Addition and multiplication are commutative, so the order of the numbers does not matter. Subtraction is not: 5 minus 3 and 3 minus 5 give different answers.
Q5.Which property of addition is at work in (57 + 63) + 14 = 57 + (63 + 14)?Tap to reveal
Answer: The associative property
Associativity is about regrouping rather than reordering. It is the rule that lets you add a long column of numbers in whatever chunks are easiest and still land on the same total.
Q6.What is the name of the property shown by 12 + 0 = 12?Tap to reveal
Answer: The identity property of addition
Zero is the identity element for addition. Multiplication has one too: any number times 1 is left unchanged.
Q7.What is the greatest common factor of 24 and 36?Tap to reveal
Answer: 12
24 breaks down into 2 x 2 x 2 x 3 and 36 into 2 x 2 x 3 x 3. The factors they share are 2, 2 and 3, and 2 x 2 x 3 = 12.
Q8.What is the least common multiple of 5, 6 and 10?Tap to reveal
Answer: 30
30 is the first number that appears in the 5, 6 and 10 times tables at once. Multiplying all three together gives 300, which is a common multiple but not the smallest one.
Q9.What kind of fractions are 4/4, 9/8 and 7/4?Tap to reveal
Answer: Improper fractions
An improper fraction has a numerator at least as large as its denominator, so its value is 1 or more. Rewritten as a mixed number, 9/8 becomes 1 and 1/8.
Famous formulas and theorems
Every one of these six formulas is something a general audience has met, even if the name has slipped. Read the equation out and ask for the name, or read the name and ask what the letters mean — both directions work as a quiz round.
Two of them are worth pausing on. The law of cosines is not a separate rule to memorise but the Pythagorean theorem stretched to cover any triangle, and Fermat's Last Theorem is the one entry on this page that went unproven for more than three centuries.
Q1.What equation states the Pythagorean theorem?Tap to reveal
Answer: a² + b² = c²
a and b are the two short sides of a right triangle and c is the hypotenuse. Babylonian scribes were already listing whole-number triples that fit the rule on the clay tablet known as Plimpton 322, more than a thousand years before Pythagoras was born.
Q2.Which law generalises the Pythagorean theorem to any triangle, not just right-angled ones?Tap to reveal
Answer: The law of cosines
It reads c² = a² + b² − 2ab·cos C. When angle C is a right angle its cosine is zero, the final term disappears and the formula collapses straight back into Pythagoras.
Q3.Which famous theorem states that x^n + y^n = z^n has no solution in positive whole numbers when n is greater than 2?Tap to reveal
Answer: Fermat's Last Theorem
Fermat noted in a book margin around 1637 that he had a proof but not enough room to write it. Andrew Wiles, working at Princeton, finally proved it in the 1990s, more than 350 years later.
Q4.What shape does the equation x² + y² = r² draw on a graph?Tap to reveal
Answer: A circle, centred on the origin with radius r
It is the Pythagorean theorem in disguise: the equation says every point on the curve sits exactly r units from the centre.
Q5.In the formula C = πd, what do C and d stand for?Tap to reveal
Answer: The circumference and the diameter of a circle
Divide any circle's circumference by its diameter and the answer is always pi, whether you measure a coin, a dinner plate or the equator.
Q6.What does the equation y = mx + b represent, and what are m and b?Tap to reveal
Answer: A straight line, where m is the slope and b is the y-intercept
British and Australian textbooks write the same line as y = mx + c, so which letter stands for the intercept depends on where you went to school.
Number sequence puzzles
Each of these sequences has a number missing, and most of them do not follow a single rule — that is the trick. Two or three rules take turns, so a run that looks like it is doubling suddenly adds instead. One sequence in the round does run on a single rule, but the step itself grows each time. Either way the pattern only shows up once you write the steps between the numbers rather than staring at the numbers themselves.
That is the method: subtract or divide each pair of neighbours and write the results in a row. If the steps alternate, or climb by a fixed amount each time, you have found the rule. Paper helps more here than anywhere else on the page, so give people a full minute each.
Q1.What number is missing? 3, 6, 7, 14, 15, ___, 31, 62, 63Tap to reveal
Answer: 30
The rule alternates between doubling and adding 1. 15 doubled is 30, and 30 plus 1 gives the 31 that follows.
Q2.What number is missing? 4, 20, 24, ___, 44, 60, 64Tap to reveal
Answer: 40
Two steps take turns, add 16 then add 4: 24 + 16 = 40, and 40 + 4 = 44.
Q3.What number is missing? 5, 10, 20, ___, 50, 55, 110Tap to reveal
Answer: 25
The sequence alternates between adding 5 and doubling: 20 + 5 = 25, and 25 doubled is 50.
Q4.What number is missing? 6, 18, 36, ___, 216, 648, 1296Tap to reveal
Answer: 108
The multipliers alternate between 3 and 2: 36 x 3 = 108, then 108 x 2 = 216.
Q5.What number is missing? 8, 16, 28, 44, ___, 88, 116, 148, 184Tap to reveal
Answer: 64
Here a single rule runs the whole way, but the step grows by 4 each time: 8, 12, 16, 20, 24, 28 and so on. After 44 you add 20 to reach 64, then 24 to reach 88.
Q6.What number is missing? 3, 6, 18, 36, ___, 216, 234, 468, 1404Tap to reveal
Answer: 72
Three rules rotate in a loop — double, triple, add 18. The number 36 lands on the doubling step, giving 72, which tripled gives 216.
Probability, odds and counting
Cards and dice are where most people first meet probability, and this round sticks to questions you can check in your head or on the back of an envelope. The counting questions at the end are the useful ones: they explain why a four-digit PIN is ten times harder to guess than a three-digit one.
Watch out for the question about three players. Almost everyone starts calculating, when the fastest route is to notice that two of the three targets cannot happen at all.
Q1.One card is drawn at random from a shuffled 52-card deck with the jokers removed. What is the probability that it is a diamond?Tap to reveal
Answer: 1 in 4
13 of the 52 cards are diamonds, and 13/52 reduces to 1/4. The odds are identical for any one of the four suits.
Q2.Two cards are drawn from a 52-card deck without putting the first one back. What is the probability that both are red?Tap to reveal
Answer: 25 in 102, or about 24.5%
The first card is red with probability 26/52. With one red card already gone, the second is red with probability 25/51. Multiply the two and 26/52 x 25/51 reduces to 25/102.
Q3.You roll two fair dice. What is the probability that they total 7?Tap to reveal
Answer: 1 in 6
Six of the 36 possible rolls make seven: 1+6, 2+5, 3+4 and each of those reversed. No other total has as many ways of happening, which is why 7 turns up more often than anything else.
Q4.Player A must draw three aces from a 52-card deck, player B must roll 13 with two dice, and player C must roll a total of 2 with three dice. Who has the best chance?Tap to reveal
Answer: Player A
A's chance is slim — 1 in 5,525 — but B and C are attempting the impossible. Two dice cannot reach 13, and three dice cannot total less than 3.
Q5.A 'combination' lock uses three numbers, each anywhere from 0 to 39. How many different combinations are possible?Tap to reveal
Answer: 64,000, which is 40 x 40 x 40
Each of the three positions has 40 choices, so the count is 40³. A mathematician would call these permutations rather than combinations, because the order of the three numbers matters.
Q6.A nine-digit code is chosen at random, each digit anywhere from 0 to 9. What is the chance it matches one particular code?Tap to reveal
Answer: 1 in 1,000,000,000
Ten choices in each of nine slots gives 10⁹, a billion possible codes. Each extra digit multiplies the number of possibilities by ten, which is why one more character makes a PIN so much harder to guess.
Hard math trivia: pi, e and the famous constants
This is the round for the people who wanted math trivia to be difficult. It covers the two constants that turn up everywhere: pi, known in some form for nearly four thousand years, and e, which only entered mathematics in the 1600s and is just as unavoidable.
Neither is the root of any ordinary polynomial equation with whole-number coefficients — both are what mathematicians call transcendental. Hermite proved it for e in 1873, and nine years later Lindemann adapted his method to prove the same of pi. It was that second proof, and only that one, which closed a question the ancient Greeks had left open. Two of the questions below are about those proofs.
Q1.Babylonian mathematicians were already using a value for pi around 1900 BC. Which fraction did they use?Tap to reveal
Answer: 25/8, which is 3.125
That is about half a percent below the true value. It comes from a clay tablet found at Susa, on which the scribe compares a hexagon’s perimeter with the circle drawn around it. The Babylonians wrote in base 60 rather than base 10, so the figure is really 3;7,30 in their notation — crude by modern standards, but close enough for the building work it was used for.
Q2.Which three-digit run famously makes its first appearance at decimal place 2,440 of pi?Tap to reveal
Answer: 666
Digit hunters enjoy the coincidence, but it means nothing mathematically. Search far enough into pi's endless decimals and short strings like this keep cropping up.
Q3.A domed ‘Pi Room’ whose cupola is covered in 707 hand-calculated digits of pi belongs to which Paris science museum?Tap to reveal
Answer: The Palais de la Découverte
The cupola was decorated in 1937 with William Shanks’s 707 digits, all worked out by hand and published in 1873. Only the first 527 were right — Shanks slipped at the 528th place, and the error went unnoticed until the 1940s, after which the wrong digits were repainted. The museum itself is closed for a six-year rebuild and is due to reopen in March 2027.
Q4.What does the Japanese term 'enshuritsu' mean?Tap to reveal
Answer: Pi — it translates literally as 'circle circumference ratio'
Several languages describe the constant rather than borrow a Greek letter for it, and this one spells out the definition: the ratio of a circle's circumference to its diameter.
Q5.Which 18th-century probability problem, named after a French count, lets you estimate pi by dropping needles onto a lined floor?Tap to reveal
Answer: Buffon's needle problem
Drop a needle shorter than the gap between the lines and the chance it crosses a line works out as 2L divided by pi times d. Count enough crossings and you can work backwards to pi — an early example of what we now call a Monte Carlo method.
Q6.What is the formula for the period — the swing time — of a pendulum making a small swing?Tap to reveal
Answer: T = 2π√(L/g)
L is the pendulum’s length and g is the strength of gravity, and pi is in there because a small swing is a slice of circular motion. The same reasoning is why the constant shows up in waves, springs and alternating current.
Q7.Who proved in 1882 that pi is transcendental, meaning it is not the root of any polynomial equation with rational coefficients?Tap to reveal
Answer: Ferdinand von Lindemann
His proof finished off a puzzle about 2,000 years old. Squaring the circle — building a square of equal area with only a ruler and compass — is not merely hard but impossible.
Q8.In which TV series does a science officer defeat an alien by ordering the ship's computer to compute pi to its last digit?Tap to reveal
Answer: Star Trek
Spock pulls the trick in the 1967 episode 'Wolf in the Fold'. The order can never be completed, which is exactly the point: pi's decimals go on forever.
Q9.How is the sentence 'Sir, I send a rhyme excelling in sacred truth and rigid spelling' connected to pi?Tap to reveal
Answer: It is a mnemonic — the number of letters in each word gives pi's digits
Count them and you get 3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8. Writing pi this way has its own name, piphilology, and the longest attempts run to thousands of words.
Q10.Can the constant e be written exactly as a fraction?Tap to reveal
Answer: No — e is irrational, so no ratio of two whole numbers equals it
e begins 2.718281828459045 and never settles into a repeating pattern. The tempting 1828 that appears twice near the start is a coincidence, and it has fooled plenty of students into thinking the digits repeat.
Q11.The letter e was not taken from Euler's surname. What word is it generally thought to stand for?Tap to reveal
Answer: Exponential
Euler used the symbol in a 1731 letter to Christian Goldbach and never explained the choice. ‘Exponential’ is the usual guess; historians also point out that e is simply the next vowel after a, which Euler was already using for something else. What is certain is that he did not name it after himself — that would have been badly out of character.
Q12.What is the name of the equation e^(iπ) + 1 = 0?Tap to reveal
Answer: Euler's identity
One short line ties together five of the most important numbers in mathematics: e, i, pi, 1 and 0. A readers' poll in the journal The Mathematical Intelligencer once voted it the most beautiful theorem in all of mathematics.
Q13.What is e the base of?Tap to reveal
Answer: The natural logarithm, written ln
Choosing e as the base is what makes calculus tidy: the curve y = ln x has a slope of exactly 1/x at every point, and no other base gives an answer that clean.
Q14.What did the French mathematician Charles Hermite prove about e in 1873?Tap to reveal
Answer: That e is transcendental
Joseph Liouville had already shown that e cannot satisfy a quadratic equation with whole-number coefficients. Hermite's method was the toolkit Lindemann adapted nine years later to settle the same question for pi.
Q15.What is the derivative of y = e^x?Tap to reveal
Answer: e^x — the function is its own derivative
Apart from multiples of itself, no other function behaves this way. It is the reason e appears whenever something grows at a rate proportional to its own size, from compound interest to a bacterial culture.
Frequently Asked Questions
What makes a good math trivia question?
The fact should be more interesting than the arithmetic. Nobody wants to be asked for 17 times 23 at a quiz night, but they will happily argue about whether the Babylonians knew pi, or why two dice land on 7 more often than any other total. A good math question is answered in a sentence and leaves you with something to repeat afterwards, which is why every answer on this page comes with a short explanation.
Do you need to be good at math to play?
No, though two rounds ask you to work something out. The number-sequence round rewards a pencil — write down the gap between each pair of numbers and the alternating rule usually becomes obvious — and the card questions in the probability round are one multiplication each. Nothing on the page needs a calculator. The opening round is recall, and if you would rather skip arithmetic entirely, the pi and e round is pure general knowledge dressed up as mathematics.
What is the hardest question on this page?
The one about three players, where A needs three aces, B needs to roll 13 with two dice and C needs to roll a total of 2 with three dice. Nearly everybody starts calculating probabilities and misses the shortcut: two dice cannot reach 13 and three dice cannot total less than 3, so both of those chances are zero and A wins with his slim 1 in 5,525. The sequence puzzle with three rotating rules — double, triple, add 18 — comes a close second.
How do I run a math trivia round at a quiz night?
Use one section as a round. Four of them run to six or nine questions, which is about right; the long pi and e round splits neatly into two halves of seven and eight. Give each team paper, read the question twice, allow about 30 seconds, and a full minute for anything in the sequence round. Read the explanation out when you give the answer, because it is what stops a math round feeling like a test. Mixing one easy round with the pi and e round works better than a whole evening of mathematics.
Why does pi show up in formulas that have nothing to do with circles?
Because so much of physics is circular motion in disguise. A pendulum's swing, a vibrating spring, a sound wave and alternating current can all be described by going round and round a circle at a steady rate, so the constant that measures a circle comes along with them. Pi also appears in pure probability — in Buffon's needle problem and in the bell curve of the normal distribution — which is one of the reasons mathematicians find it so strange.
Are there easier math questions for children?
Yes. This page is written for adults and teenagers, and the final round is deliberately difficult. For a version aimed at children aged 6 to 12, with rounds on counting, shapes, measurement and money, use the math trivia questions for kids page instead. The free quiz on that page works the same way and needs no signup.
