145 Fun Facts About Multiplication

Which property of multiplication says 3 × 4 and 4 × 3 give the same product, no matter the order?

Commutative Property: turn 3 rows of 4 dots on their side and they become 4 rows of 3, still 12 dots in all, which is why swapping the order can never change the answer.

Multiplying two negative numbers together always gives what kind of result?

A positive number: follow the pattern 2 × −3 = −6, 1 × −3 = −3, 0 × −3 = 0, and the next step down, −1 × −3, has to climb to +3.

Which old trading word names a dozen dozens, or 144 of anything?

A gross is 144 items, a name taken from the Old French for 'large dozen'; a dozen gross, 1,728, is a great gross.

Which property says (2 × 3) × 4 and 2 × (3 × 4) give the same result, whatever the grouping?

Associative: because the grouping never matters, 7 × 25 × 4 can be done as 7 × 100, the regrouping trick behind many mental-arithmetic shortcuts.

Which property of multiplication lets a(b + c) be expanded to ab + ac?

The Distributive Property spreads a factor across every term in the brackets; it's why 7 × 12 can be done as 7 × 10 plus 7 × 2.

Which mathematician is widely credited with introducing the '×' symbol for multiplication in 1631?

William Oughtred, a Surrey rector who taught mathematics in his spare time, printed × in his 1631 Clavis Mathematicae; algebra later sidelined the cross because it is so easily mistaken for the letter x.

Which multiplication method, also called the Italian or gelosia method, writes the digits round a box of cells and sums its diagonals?

Lattice multiplication writes each single-digit product in its own cell and leaves every carry for the diagonal sums at the end, so nobody has to multiply and carry at the same time.

Which civilization multiplied by 'doubling and halving' using powers of two?

Egyptian scribes needed no times table: they doubled one number again and again, then added up the doublings that matched the other number's powers of two.

Which number is the multiplicative identity, leaving any number multiplied by it unchanged?

Multiplying any number by 1 leaves it unchanged, which is why 1 is called the multiplicative identity; 0 plays the same role for addition.

Which result states every integer over 1 is prime or a unique product of primes, up to order?

The fundamental theorem of arithmetic is one reason 1 is not counted as a prime: if it were, 12 could be 2 × 2 × 3 or 1 × 2 × 2 × 3, and no number would have just one factorisation.

Which easier operation do logarithm tables let you substitute for multi-digit multiplication?

Addition: since log(ab) = log a + log b, you add the two logarithms from the table and look up the antilog to get the product; division becomes subtraction.

Which Scottish mathematician built numbered calculating rods and named the technique rabdology?

John Napier engraved a times table on the faces of each rod, so lining up the rods for 4, 2 and 5 lets you read off 425 × 7 with only a few small sums; the sets became known as Napier's bones.

Which hand-operated calculator uses logarithmic scales to multiply and divide?

The slide rule, born in the 17th century, still flew with the Apollo crews, yet once pocket calculators became cheap in the mid-1970s it was soon obsolete.

The oldest known multiplication tables, from about 4,000 years ago, were used by which civilization?

The Babylonians pressed their tables into clay some 4,000 years ago, but in base 60 rather than base 10, the same way of counting that still gives us 60 minutes in an hour.

The world's earliest known decimal multiplication table, made in China around 305 BC, was written on what?

Bamboo slips: the 21 strips reached Tsinghua University in 2008 muddy, mouldy and mixed in with nearly 2,500 others, and historians had to piece the table together like a jigsaw.

In French, Italian and Russian, the multiplication table is named after which Greek?

Pythagoras: French 'table de Pythagore' and Italian 'tavola pitagorica' keep his name, though the credit is tradition rather than proven fact.

Which word means to multiply something by four?

Quadruple comes from the Latin for 'fourfold', and the same 'fold' is hidden inside 'multiply' itself, which goes back to the Latin multiplex, 'many-fold'.

Which property says the product of any two integers is itself an integer?

Closure: the integers are closed under multiplication, so 7 × (−3) = −21 stays an integer, whereas they are not closed under division, since 7 ÷ 3 is not.

England's national curriculum expects pupils to know their times tables up to which fact by the end of Year 4?

12 × 12: Year 4 pupils in England's state schools sit an on-screen check of 25 timed questions to show they can recall the tables up to 12.

The Chinese eighty-one-sentence rhyme for learning products was historically known by what name?

The nine-nine table: early versions are said to have opened with 'nine nines beget eighty-one' and counted down from there, which gave the rhyme its name; Chinese pupils still learn it by heart.

If two numbers multiply together to make zero, what must be true of them?

At least one is zero: this zero-product property is what lets (x − 5)(x − 3) = 0 be split into two easy cases, x = 5 or x = 3.

Two numbers that multiply to make exactly 1, such as 4 and ¼, are called what?

Reciprocals: flip a fraction to find its partner, which is why dividing by ½ gives the same answer as multiplying by 2.

Multiplying a number by itself and then by itself again, as in 4 × 4 × 4, gives its what?

Cube: 4 × 4 × 4 = 64 counts the unit blocks in a cube four blocks long, wide and high, which is where the name comes from.

Which word describes a whole number, such as 12, that can be made by multiplying two smaller whole numbers?

Composite: 12 counters can be laid out as 3 rows of 4, while a prime such as 13 only ever makes one long line.

Which operation asks what number, multiplied by itself, gives 81?

Square root: 81 gives a tidy 9, but 2 has no such answer, since its square root is a decimal that never ends or repeats and so can't be written as a fraction.

Who, in 1698, proposed a middle dot for multiplication because × looked too much like x?

Gottfried Wilhelm Leibniz told Johann Bernoulli in a 1698 letter that × was too easily confused with x; the dot he preferred is still the usual multiplication sign in German mathematics.

In computer programming, which symbol is the usual notation for multiplication?

The asterisk became the stand-in because early computer character sets such as ASCII had no × sign, and it has kept its place on the numeric keypad ever since.

In a screen size such as 1920 × 1080, the multiplication sign is read aloud as which word?

By: the sign is read 'times' in a sum but 'by' in a size, though multiplying anyway gives the screen's pixel count, 1920 × 1080 = 2,073,600.

In a famous legend, wheat grains doubled on each square of which board add up to more than the world grows?

A chessboard: one grain doubled across 64 squares comes to more than 18 quintillion grains, far more wheat than the whole world harvests in a year.

Rules for multiplying with zero and negative 'debts' were set out in 628 AD in which country?

India: Brahmagupta's Brahmasphutasiddhanta treated zero as a number like any other, stating flatly that a number multiplied by zero becomes zero.

Who popularized place-value decimal arithmetic in the West in the 13th century?

Fibonacci: his Liber Abaci of 1202 showed Italian merchants how to calculate with Hindu-Arabic numerals and place value instead of Roman numerals and the abacus.

The grid method splits 34 × 13 into the partial products 300, 90, 40 and which fourth number?

12, from 4 × 3: the grid breaks 34 into 30 + 4 and 13 into 10 + 3, multiplies each pair in its own box, and the four boxes add up to 442.

Multiplying two huge primes is easy but undoing it is so hard that the gap protects which everyday technology?

Internet encryption: the RSA system publishes the product of two secret primes hundreds of digits long, trusting that no computer can split it back into them in any useful time.

In modern English usage, a million multiplied by a million makes which number?

A trillion: six zeros times six zeros gives twelve, though on the old British 'long scale' a million million was called a billion.

In which number system is the whole times table just 0 × 0, 0 × 1 and 1 × 1?

Binary has just two digits, so multiplying comes down to copying and shifting rows and then totalling them, which is how a computer chip does it.

Multiplying a number by itself repeatedly gives powers; stacking powers on powers gives which operation?

Tetration is the next step up from powers, and it grows so fast that a tower of just four 2s already comes to 65,536.

A quick way to multiply any number by 5 is to multiply it by 10 and then do what?

Halve the result: 5 is half of 10, so 48 × 5 becomes 480 ÷ 2 = 240, two steps most people can do in their heads.

Multiplying (a + b) by (a − b) always gives which tidy result?

The difference of two squares, a² − b²: the middle terms cancel, which gives a handy mental trick, since 19 × 21 is (20 − 1)(20 + 1) = 400 − 1 = 399.

The symbol ∏ used for the product of a sequence derives from which Greek letter?

Pi: ∏ is the capital Greek letter pi, standing for 'product', just as the summation sign ∑ is capital sigma for 'sum'.

In a multiplication, what is the technical name for the number that is being multiplied?

The multiplicand is the number being multiplied and the multiplier is the number it is multiplied by; since order does not matter the distinction is mostly academic.

In algebra, what is the 3 in the expression 3xy² called?

The coefficient is the number multiplying the letters; when none is written it is taken to be 1, which is why x + x makes 2x.

Which mark after a number means 'multiply it by every smaller whole number down to 1'?

Exclamation mark: in 1808 Christian Kramp wanted a 'very simple notation' for a product he used constantly, so 5! means 5 × 4 × 3 × 2 × 1 = 120, a factorial.

The Ishango bone, sometimes cited as a hint of prehistoric multiplication, was found where?

Central Africa: the bone, found at Ishango in what is now DR Congo, is about 20,000 years old, and one column of its notches has been read as a doubling pattern, though others see only a tally or a calendar.

A rectangle of dots in equal rows and columns, used to picture 3 × 4 in class, is called what?

An array: because every row holds the same number, rows times columns gives the total at once, the same idea that gives a rectangle its area.

Jakow Trachtenberg developed his rapid mental-calculation system while held where?

A Nazi concentration camp: the Odessa-born engineer worked out his rules there to keep his mind occupied, and they were later published as the Trachtenberg Speed System.

Henri Genaille, who invented carry-free multiplication rulers in 1891, worked as what?

A railway engineer: Genaille's rulers are a variant of Napier's bones that show the carry graphically, so products can be read off with no mental arithmetic.

Which mathematical objects usually give a different answer when multiplied in the opposite order?

Matrices: A × B and B × A usually differ, and sometimes only one of the two can be worked out at all, because the columns of the first must match the rows of the second.

In which counting game do players say a word instead of any number in the 3 or 5 times tables?

Fizz buzz: players say 'fizz' for the 3s and 'buzz' for the 5s, and writing a program to play it became a well-known first hurdle in programmers' job interviews.

Which mnemonic reminds American students to multiply before they add?

PEMDAS puts multiplying ahead of adding, so 2 + 5 × 3 is 17, not 21; but the M does not outrank the D, since multiplying and dividing rank equally and run left to right.

In algebra, writing 3x with no sign between the 3 and the x shows multiplication by what?

Juxtaposition, simply placing things side by side, saves ink but starts arguments, since calculators disagree on whether 6 ÷ 2(1 + 2) comes to 9 or 1.

In botany, a × placed between two plant names marks the plant as what?

A hybrid: the sign marks a cross between two parent plants, so the grapefruit, an accidental cross of sweet orange and pomelo, is formally Citrus × paradisi.

On binoculars marked 8×42, what does the 8× tell you?

The magnification: 8× makes things look eight times closer, while the 42 is the width of each front lens in millimetres, which sets how much light gets in.

In Roman numerals, V multiplied by X gives which numeral?

L: V times X is 5 × 10 = 50, but with no place value the numerals were mainly for recording results, so Romans did the multiplying itself on an abacus.

How old was Anatoly Karatsuba when, as a student, he found his fast multiplication method?

23: Karatsuba, born in January 1937, found the method in the autumn of 1960, within a week of Kolmogorov stating his conjecture at a Moscow seminar.

Multiply 100 copies of the number 10 together and you get which number, a 1 followed by 100 zeros?

A googol: the name was coined by a nine-year-old, Milton Sirotta, whose uncle, the mathematician Edward Kasner, then put it into print.

Doubling both the length and the width of a rectangle multiplies its area by what?

4: each doubling multiplies the area by 2, and 2 × 2 = 4, which is why a 16-inch pizza is as much food as four 8-inch ones.

Multiplying two positive fractions that are each less than 1 always gives an answer that is what?

Smaller than both: half of a half is a quarter, because taking a fraction of a fraction can only shrink it, so multiplying does not always make things bigger.

To multiply 45 by 11 in your head, a shortcut writes 4 and 5 with what between them?

Their sum: 4 + 5 = 9 goes in the middle to give 495, because 45 × 11 is just 450 + 45; if the middle passes 9, the extra 1 is carried left.

Multiplying the imaginary unit i by itself gives which real number?

Minus one: no ordinary number does that, but picture multiplying by i as a quarter turn and it makes sense, since two quarter turns leave you facing backwards.

In the 9 times table up to 9 × 10, the digits of every answer always do what?

Add up to 9: each step up the table adds 10 and takes away 1, so the first digit climbs as the last digit drops and the pair always totals 9, a quick way to spot a slip.

Multiplying 6 by 6 gives 36, the number of different outcomes when you roll what?

Two dice: each of the 6 faces of one can pair with any of the 6 on the other, and since only one of those 36 pairs is a double six, it turns up about once in 36 rolls.

Multiplying every whole number from 52 down to 1 counts the ways to order a card deck; how long is the answer?

68 digits: the total is roughly an 8 followed by 67 zeros, so vast that two properly shuffled decks will almost certainly never come out in the same order.

Which metric prefix multiplies a unit by one million?

Mega, from the Greek for 'great', multiplies by a million, so a megawatt is a million watts; kilo multiplies by only a thousand, and micro divides by a million.

In 2⁴, shorthand for 2 × 2 × 2 × 2, what is the small raised 4 called?

The exponent counts how many 2s are multiplied together, and each extra one doubles the result, so 2⁴ is only 16 but 2²⁰ is already over a million.

In the FOIL method for multiplying binomials, what does the O stand for?

Outer: FOIL lists the four products, First, Outer, Inner, Last, so that none is forgotten, but it only fits two-term brackets and breaks down as soon as one bracket has three terms.

Which scribe copied out the Rhind papyrus, the main source for Egyptian doubling multiplication?

Ahmes copied the Rhind papyrus around 1550 BC from an older text; it and the Moscow papyrus preserve the method, which needs only doubling, halving and adding.

To find 10% of any number, you can multiply it by what?

0.1: per cent means 'out of a hundred', so 10% is 10/100 = 0.1, whereas multiplying by 1.1 adds that 10% on top of the original.

Which two numbers are the only ones that stay the same when multiplied by themselves?

0 and 1 are the only numbers equal to their own squares, which suits computer logic, where the two stand for false and true and the AND operation is simply multiplication.

Multiplying 60 × 60 × 24 gives 86,400, the number of seconds in what?

A day: 60 seconds × 60 minutes × 24 hours, which means a million seconds lasts only about eleven and a half days while a billion takes nearly 32 years.

Which author made 'what do you get if you multiply six by nine' the Ultimate Question of Life, the Universe and Everything?

Douglas Adams gave the answer as 42, and when fans noticed that 6 × 9 really does come to 42 in base 13, he brushed off any hidden meaning with a curt 'As if.'

Which US body's 1989 standards urged less rote memorisation of times tables?

The National Council of Teachers of Mathematics later clarified in 2006 that basic facts must still be learned, without settling how.

Multiply 6 by any even digit, such as 4 or 8, and the answer always ends in what?

That same digit: 6 × 2 = 12, 6 × 4 = 24, 6 × 6 = 36 and 6 × 8 = 48, because five lots of an even number always end in zero, leaving the sixth lot to set the last digit.

Despite its name, going up one octave multiplies a note's frequency by what?

Two: the 'eight' in octave counts the notes of the scale from one C to the next, while in physics each octave simply doubles the frequency.

Which 'human computer' multiplied two random 13-digit numbers in 28 seconds at Imperial College London in 1980?

Shakuntala Devi was about three when her father, a circus trapeze artist and lion tamer, spotted her memory for numbers over a pack of cards, and he was soon touring her gift in road shows.

The French word for 80, 'quatre-vingts', literally multiplies which two numbers?

Four and twenty: French keeps a trace of counting in twenties, just as English once did with 'four score', though in parts of Switzerland 80 is simply 'huitante'.

In darts, the highest score from one dart is 60, beating the bullseye's 50; where on the board is it?

The triple 20: the narrow inner ring multiplies a segment's score by three, so 3 × 20 = 60 beats the bullseye, and three of them make the maximum 180.

Scientists call a tenfold increase, a multiplication by ten, one order of what?

Magnitude: each order multiplies by ten again, so three orders of magnitude means a thousand times bigger, the gap between a millimetre and a metre.

Ten 2s multiplied together give which number, familiar from computer memory sizes?

1,024: because it is so close to 1,000, computing borrowed the prefix kilo for it, which is why a kilobyte was long counted as 1,024 bytes rather than 1,000.

In the finger trick for 7 × 8, the touching fingers and those below count as what?

Tens: for 7 × 8, touch the 7-finger to the 8-finger; the 2 + 3 touching-and-below fingers give 50, and the 3 × 2 fingers above give 6, so 56.

Multiplying 142,857 by any number from 2 to 6 does what to its six digits?

Rotates them in order: 142,857 × 2 is 285,714 and × 3 is 428,571, a merry-go-round that only stops at × 7, which gives 999,999.

Which technique solves a/b = c/d by multiplying each top by the other fraction's bottom?

Cross-multiplication turns a/b = c/d into ad = bc, which works because it is one fair move in disguise: multiply both sides by b × d and each bottom cancels.

Multiplying a steady speed by the time spent travelling gives which quantity?

Distance: the units multiply too, so miles per hour times hours leaves plain miles, the hours cancelling just as numbers would.

Which kind of interest multiplies a balance by the same factor every year, so that growth itself earns growth?

Compound interest multiplies where simple interest only adds, so money growing at 7% a year doubles in about ten years rather than fourteen.

Multiplying 111,111,111 by itself gives an answer with which striking pattern?

It counts 1 to 9 and back: the answer is 12,345,678,987,654,321, and the smaller versions work the same way, since 11 × 11 = 121 and 111 × 111 = 12,321.

Rounding 198 × 52 to 200 × 50 gives a quick estimate of which answer?

10,000: the true answer is 10,296, so the estimate is within 3%, close enough to catch a slipped decimal point or a mistyped calculator key.

In arithmetic 'of' usually means multiply, so half of a third is which fraction?

One sixth: multiply the tops and multiply the bottoms, 1 × 1 over 2 × 3, which is like cutting each third of a cake in two to make six equal slices.

A penny that doubles every day for 30 days ends up worth roughly how much?

About $5 million: 29 doublings turn one cent into $5,368,709.12, yet on day 20 it is still only about $5,000, which is why doubling fools the intuition.

Plato set his ideal city's citizens at which factorial, partly because it divides so many ways?

5,040 is 1 × 2 × 3 × 4 × 5 × 6 × 7 and has 60 divisors, including every number from 1 to 10, so Plato's citizens could be split evenly for war, tax or land in dozens of ways.

Robert Recorde's 16th-century term 'zenzizenzizenzic' referred to which power of a number?

Zenzic meant squared, so squaring three times gives the eighth power. His fifth power was the sursolid and his seventh the second sursolid.

Archimedes proved the law 10^a × 10^b = 10^(a+b) in which of his works?

The Sand Reckoner: Archimedes needed the rule to handle enormous powers of ten while estimating how many grains of sand would fill the universe.

Laplace said logarithms, by shortening long multiplications, doubled the life of whom?

The astronomer: Laplace called logarithms an admirable artifice which, by reducing to a few days the labour of many months, doubles the life of the astronomer and spares him the errors of long calculations.

In base 10, a perfect square can end in which of these digits?

6: squares end only in 0, 1, 4, 5, 6 or 9, so any number ending in 2, 3, 7 or 8 can be ruled out as a perfect square at a glance.

What name describes an algorithm, like the fastest known multiplication method, that only wins on impossibly large inputs?

Galactic algorithm: Ken Regan coined the name for Richard Lipton's idea of methods that win on paper yet will never be run on any data set on Earth.

The dot product of two vectors yields what kind of quantity?

A scalar: the dot product boils two vectors down to one plain number, and when that number is zero the two vectors are at right angles.

Which board game multiplies a word's points with 'double word' and 'triple word' squares?

Scrabble: the multipliers stack, so a word laid across two triple-word squares is tripled and then tripled again for nine times its face value, a play known as a triple-triple.

In The Hitchhiker's Guide to the Galaxy, Arthur Dent draws the question 'multiply six by nine': what is the true answer?

The true answer is 54, not the number Deep Thought made famous. Fans noticed that the book's sum does work in base 13, a theory Douglas Adams brushed off.

Which American children's TV series began by setting the times tables to songs such as 'Three Is a Magic Number'?

Schoolhouse Rock grew from an adman's worry that his son knew Rolling Stones lyrics by heart but struggled with his tables. Musician Bob Dorough wrote the first songs.

The United States flag has five rows of six stars and four rows of five: how many stars altogether?

The 50 stars stand for the states, in a design adopted after Hawaii's admission. The 13 stripes represent the colonies that won independence.

Which Adele album, home to the hit single 'Hello', has a title that is the answer to five times five?

25 reflects Adele's life and frame of mind at that age, and American fans bought 3.38 million copies in its first week on sale.

The French word quatre-vingts literally means 'four twenties': which number does it name?

It names 80, a survival of an older habit of reckoning in twenties. The same habit turns 87 into quatre-vingt-sept, literally 'four-twenties-seven'.

By the popular rule that one human year equals seven dog years, how old in dog years is a 9-year-old dog?

The rule gives 63, but it is a popular myth. A dog's first year is nearer 15 human years, the second about nine, and each year after that about five.

San Francisco's NFL team is named after gold-rush prospectors: which answer to seven times seven is in the team's name?

Seven sevens are 49, and the 49ers honour the prospectors who rushed to California in 1849. The team's first logo showed a gold miner firing two pistols.

The poem 'A Visit from St. Nicholas' gives Santa eight reindeer: how many legs do the eight have between them?

The eight reindeer share 32 legs, and Rudolph is not among them. He joined the team more than a century later, in a 1939 story.

Following the order of operations taught as PEMDAS or BODMAS, what is the value of 7 + 2 × 5?

The value is 17, because multiplying comes first: 2 × 5 makes ten, and only then is the 7 added. Working left to right gives the tempting wrong answer of 45.

Which storybook heroine, created by an Oxford maths lecturer, frets that 'four times five is twelve'?

Alice muddles her tables in Wonderland, sighing that she 'shall never get to twenty at that rate'. Lewis Carroll held a mathematics lectureship at Christ Church for 26 years.

A chessboard is laid out in eight rows of eight squares: how many squares does that make in total?

The 64 squares alternate light and dark, and the board is always turned so that each player has a light square in the near-right corner.

A standard deck of playing cards has four suits of 13 cards each: how many cards is that without jokers?

The 52 cards form the most common pack in the world, with a king, queen and jack in every suit. Makers often add anything from one to six jokers.

In darts, the treble ring triples a segment's value: what do three darts in the treble 20 score in total?

The maximum 180 brings the house down: on television the referee announces it in exuberant style. Darts players call 100 points a ton.

A classic Sudoku puzzle is a grid of 9 rows and 9 columns: how many cells does the whole grid contain?

The grid holds 81 cells, split into nine 3×3 boxes. The name was shortened in 1986 from a Japanese phrase meaning 'the numbers must be single'.

A soccer match is played over two halves of 45 minutes: how many minutes is that before any stoppage time?

The 90 minutes rarely end on the dot: the referee adds stoppage time for injuries and substitutions, and the ball is typically in play for only about an hour.

A spider walks on eight legs, two more than any insect: how many legs do seven spiders have between them?

Seven spiders have 56 legs, a sum with a built-in memory aid: 5, 6, 7, 8 run in order, and 56 is 7 × 8. Each spider leg is made of seven distinct parts.

A gross, from the Old French for 'large dozen', means a dozen dozens: how many items is that?

One gross is 144, and a dozen of those makes a 'great gross'. The Dozenal Society of America still argues for reckoning this way instead of in decimals.

Multiplying any whole number by 2, 4, 6 or 8 always gives an answer of which kind?

An even number always results, because one even number in a multiplication is enough. Only odd times odd stays odd, as in 3 × 5 = 15.

Any whole number multiplied by five must end in one of which two digits, giving a quick divisibility test?

The last digit is always 0 or 5, taking turns as the table climbs: 5, 10, 15, 20. That makes five one of the easiest numbers to test for by eye.

The Indianapolis Motor Speedway's famous race covers 200 laps of a 2.5-mile oval: how many miles is that?

The 500 miles give the Indianapolis 500 its name, and drivers lap the oval counter-clockwise. Ray Harroun won the first running in 1911.

A men's major golf championship is played over four rounds of 18 holes: how many holes is that in all?

The 72 holes are split by a cut: after the first two rounds, only the leading players carry on to the weekend.

An NBA game is played in four quarters of 12 minutes each: how many minutes of playing time is that?

NBA regulation time is 48 minutes, whereas international games under FIBA rules use 10-minute quarters and US college men play two 20-minute halves.

A perfect game in baseball retires every batter over 9 innings of three outs: how many batters is that?

All 27 batters must go down without reaching base, a feat first called a 'perfect game' in print in 1908. Don Larsen threw one for the Yankees in the 1956 World Series.

The classic full-time working week is five days of eight hours each: how many hours of work is that?

The 40-hour week grew out of the eight-hour day movement, whose slogan split the day three ways: 'Eight hours' labour, eight hours' recreation, eight hours' rest'.

A bee has five eyes, two large compound ones and three tiny simple ones: how many eyes do seven bees have?

Seven bees have 35 eyes between them. The three small ones, called ocelli, sit between the big pair and tell the bee how bright the light is.

February in a common year lasts exactly four full weeks: how many days does that give the shortest month?

Its 28 days make February the only month that can pass without a single full moon. A leap year adds a 29th day.

An old finger-reckoning system tallies 12 finger bones on one hand five times over: what total does it reach?

The tally reaches 60: the thumb touches each bone of the four fingers to make twelve, and the other hand logs every finished dozen until five are full.

A cubic foot measures 12 inches along every edge: how many cubic inches does it hold?

A cubic foot holds exactly 1,728 cubic inches, which is 12 × 12 × 12. Engine sizes quoted in cubic inches are abbreviated c.i.d., for cubic inch displacement.

A cubic metre is 100 centimetres along every edge: how many cubic centimetres does it contain?

It contains 1,000,000 cubic centimetres, because the hundred is multiplied in three times over. That makes a cubic metre exactly 1,000 litres, and filled with water it weighs about a tonne.

By the digit-sum test for the 9 times table, which of these numbers is one of the table's answers?

126 passes because 1 + 2 + 6 makes 9, and sure enough it is 14 × 9. The test works for whole numbers of any length.

Shops that never close advertise being open '24/7': how many hours does one full week of that add up to?

A week holds 168 hours, or 10,080 minutes. Its seven days were named for the seven classical planets, a list that included the Sun and the Moon.

How many seconds are there in a normal 24-hour day, before any leap second is added?

A normal day lasts 86,400 seconds. Because the Earth's spin is slightly irregular, an occasional leap second is slipped in at the end of a day, making it one second longer.

Before decimalisation, a British pound was 20 shillings of 12 pence each: how many pence made a pound?

A pound held 240 old pence until Decimal Day, 15 February 1971, when it was redivided into 100 new pence and the shilling was abolished.

Which three-digit number, written with the same digit three times, is the answer to 3 × 37?

111 is 3 × 37, which is why every three-digit repeat such as 222 or 777 divides exactly by 37.

If every times table from 1 to 10 were continued forever, which is the first number all ten would share?

2,520 is the smallest number that divides exactly by everything from one to ten. Simply multiplying 1 to 10 together overshoots wildly, giving 3,628,800.

Which number made of nine identical digits gives 12,345,678,987,654,321 when it is multiplied by itself?

111,111,111 squared climbs to 9 and back down again. The same staircase appears on a smaller scale: 11 × 11 = 121 and 1,111 × 1,111 = 1,234,321.

Which number, the repeating decimal digits of one-seventh, just rotates its digits when multiplied by 2 to 6?

142,857 is the best-known cyclic number: doubling it gives 285,714, the same digits shifted round. Multiply it by 7 instead and the pattern breaks into 999,999.

Jules Verne's title Twenty Thousand Leagues is a distance in metric leagues of 4 km each: how many kilometres is it?

The voyage covers 80,000 kilometres, nearly twice round the Earth. The title measures how far the Nautilus travels under the seas, never how deep it dives.

The Rent song 'Seasons of Love' measures a 365-day year in minutes: how many minutes does it sing of?

The cast sings of 525,600 minutes, the length of a common year. Jonathan Larson wrote the song for his 1996 Broadway musical, and it is often known simply by that number.

Garfield Sobers was the first batsman to hit six sixes in one six-ball over of first-class cricket: how many runs?

Sobers took 36 runs off the over at Swansea in 1968, bowled by Glamorgan's unlucky Malcolm Nash. Ravi Shastri later matched the feat for Bombay.

What name is given to numbers such as 8, 125 and 1,000, each made by multiplying three copies of one whole number?

Perfect cubes take their name from geometry: exactly that many small blocks stack into one larger solid block of equal sides, as with 2 × 2 × 2 = 8.

What are numbers such as 13 and 31 called, since each appears in no times table but its own and the 1s?

Primes cannot be made by multiplying two smaller whole numbers. Euclid showed more than two thousand years ago that the supply never runs out: there are infinitely many.

Chanting '5, 10, 15, 20' aloud, a first step toward learning a times table, is a technique known as what?

Skip counting by fives names every fifth number, so the fourth one called out is 4 × 5. Older textbooks simply called it counting by twos, threes or fours.

Which old-fashioned word means 'three times', following once and twice in the sequence?

Thrice sounds dated in British and American speech, where it is often used for comic or archaic effect, yet it remains ordinary usage in Indian English.

The numbers 3, 6, 9 and 12, the first four answers in the three times table, are called what of three?

Multiples of a number come from multiplying it by whole numbers, so the list never ends. Zero qualifies too, for every number there is.

The board game Go is played on a grid of 19 lines by 19: how many points are there for placing stones?

The grid has 361 points, more than five times the squares of a chessboard. That size was already standard when Go reached Korea in the 5th century.

A Shakespearean sonnet has 14 lines of iambic pentameter, ten syllables apiece: how many syllables is that in all?

A regular sonnet runs to 140 syllables, though poets bend the rule: a pentameter line need not have exactly ten. Shakespeare's 154 sonnets first appeared together in 1609.

A Scrabble board has 15 squares along each side: how many squares does the whole board contain?

The board holds 225 squares, with the centre one often marked by a star. Architect Alfred Butts set the letter values by tallying how often letters appeared in print.

A British imperial ton is 20 hundredweight of 112 pounds each: how many pounds does that make?

The imperial or 'long' ton weighs 2,240 pounds, exactly 12% more than the American short ton, whose hundredweight really is one hundred pounds.

A mile is 1,760 yards long, with three feet in every yard: how many feet are there in a mile?

A statute mile is 5,280 feet, or exactly 1,609.344 metres. Roger Bannister first ran one in under four minutes in May 1954.