WHAT ARE YOU
THINKING OF?

Twenty is not a round number somebody picked for the sound of it. A yes-or-no answer can, at its very best, cut the field of remaining possibilities exactly in half, so twenty such answers can separate one thing from 1,048,576 of them. Call it a million. The field a player is really choosing from is far smaller than that, and that is the point: twenty questions buy comfortable headroom over any list a person could hold in mind, where ten do not reach it at all.

The odd part is the order in which that was worked out. The limit was fixed and being taught in London drawing rooms by 1786. The measure that justifies it, information as the logarithm of the number of possibilities, was not written down until the twentieth century, so a parlour convention landed on the number the mathematics would later have chosen.

Key Takeaways

• Each yes-or-no answer at best halves the field, so twenty of them reach 2 to the power of 20, which is 1,048,576 possibilities. Ten questions reach only 1,024.
• R. V. L. Hartley proposed measuring information as the logarithm of the number of possibilities in 1928; Claude Shannon named the unit the bit twenty years later, crediting the word to J. W. Tukey.
• The game was already fixed at twenty by 1786, when Hannah More described teaching "the play of twenty questions" to Sir Joshua Reynolds at a London dinner party.
• Victorian rule books admitted the limit rarely held. Cassell's 1881 collection says the object "is frequently guessed before the whole twenty questions have been asked".

Why does twenty questions stop at twenty?

Because of doubling, and because doubling gets out of hand quickly.

One question sorts the world into two piles. Two make four. Every additional question doubles the number of things you could tell apart, so the reach of the game is two multiplied by itself once for every question allowed.

Questions asked	Things they can tell apart
5	32
10	1,024
15	32,768
20	1,048,576
25	33,554,432

Ten questions is a village. Twenty is a city, which is already more than anyone can casually name. Thirty is over a billion, and forty would not be wrong so much as slack: twenty further questions spent on a field that ran out long before.

Read the table the other way and it is more useful. The first question you ask removes 524,288 possibilities. The twentieth removes one. All of the work happens early, and a question wasted at the start costs you half the game.

What is one yes-or-no answer actually worth?

There is a formal answer, and it arrived when the game was already more than 140 years old.

Writing in the Bell System Technical Journal in July 1928, the Bell Labs engineer R. V. L. Hartley set out to give information a measure an engineer could use. His conclusion, at page 540 of Transmission of Information, was to "take as our practical measure of information the logarithm of the number of possible symbol sequences", and a page later he draws out the case that matters here: "the information associated with a single selection is the logarithm of the number of symbols available", illustrated with a system offering two.

Twenty years on, Claude Shannon gave that unit its name in the same journal. "If the base 2 is used the resulting units may be called binary digits, or more briefly bits, a word suggested by J. W. Tukey," he wrote in A Mathematical Theory of Communication, adding that "a device with two stable positions, such as a relay or a flip-flop circuit, can store one bit of information. N such devices can store N bits."

One doubling is one bit, which makes the parlour game a storage problem in fancy dress. Twenty answers of yes or no are twenty binary digits, and twenty binary digits address a little over a million things, exactly as twenty two-position switches would. The binary translator shows the same idea with the switches made visible.

Who was playing twenty questions in 1786?

Hannah More, the writer and reformer, in London, at a party that also held a former prime minister.

In a letter to her sister dated 7 February 1786, printed in William Roberts's Memoirs of the Life and Correspondence of Mrs. Hannah More in 1834, she describes the evening: "Mrs. Fielding and I, like pretty little misses, diverted ourselves with teaching Sir Joshua and Lord Palmerston the play of twenty questions, and thoroughly did we puzzle them by picking out little obscure insignificant things which we collected from ancient history."

Sir Joshua is Reynolds, the painter, and Lord Palmerston is the second Viscount, father of the prime minister of the same name. Then Lord North, prime minister through the American war, "overhearing us, desired to be initiated into this mysterious game". More questioned him and reports the outcome without mercy: "his twenty questions were exhausted before he came near the truth". The answer was the earthen lamp of Epictetus, and North's reply is the best line in the letter: "I am quite provoked at my own stupidity, for I quoted that very lamp last night in the House of Commons."

Two things stand out in a letter written before anyone could put a number on information. The name and the limit are already fixed, and already being taught rather than invented. And More's winning tactic is the one the arithmetic says should not work, because obscurity does not make a field harder to halve. North was beaten by a lamp, not by the branching.

What did the Victorian rule books say about twenty questions?

That the rule was twenty, and that the rule broke constantly.

Cassell's Book of In-door Amusements, Card Games, and Fireside Fun, published in London in 1881, carries the game twice. Under "The Object Game" at pages 35 and 36, two teams race to identify the same target, and the book states the limit and then immediately qualifies it: "the number of questions asked should be limited to twenty, though in many cases it is impossible to adhere to this restriction; while, on the other hand, the object is frequently guessed before the whole twenty questions have been asked."

It also refuses to fence the subject matter. "No restriction is placed upon the objects to be thought of," the entry says, offering as fair game "a drop of water, a ray of light, a crab's claw, a nail in the boot of some great man". The book's second entry, headed "Twenty Questions" at page 49, is the version most people would recognise, with a forfeit attached to failure and the loser sent out of the room a second time. The same volume runs a section on cryptography a hundred and fifty pages later, which tells you what an evening's entertainment looked like before broadcasting, and what the ancestors of today's codes and ciphers were doing in the drawing room.

That admission of an unreliable limit is the arithmetic showing through. Twenty questions reach a million only when every answer lands on a true half-and-half split, and no real question does.

The game outlived the parlour. On 2 February 1946 a quiz built on it went out on the Mutual network in the United States, and two days later Broadcasting reported it in those exact terms: "quiz show based on parlor game 'Twenty Questions' started Feb. 2". The broadcast version made the game famous. It did not invent it, and by then the documentary record was already a hundred and sixty years long.

Why does a bad question cost more than a turn?

Because you are not paid in questions. You are paid in the ratio by which the field shrinks.

Hartley's measure makes this exact: information is the logarithm of the number of possibilities, so what a question earns is the logarithm of how much smaller it makes the pile. A perfect split earns one doubling. A question whose answer you could already predict earns close to nothing, and you cannot have the turn back.

That is why asking "is it a zebra?" in the opening rounds is so expensive. You will almost certainly hear no, and no leaves you with a field barely smaller than the one you started with: five per cent of your twenty questions gone, and none of the half-field a real question would have removed. It is also why the familiar opening triad, animal or vegetable or mineral, is a strong move rather than a tradition: a three-way split is worth up to about 1.58 doublings, more than any yes-or-no question can deliver, though only if the three categories are equally likely, and mineral swallows most of the nameable world.

Lopsidedness is where the rest of the ceiling goes. Ask whether the thing is alive and most of the nameable world says no, so a no leaves you nearly where you started. Agreeing in advance to restrict the field, to animals only, say, is worth several questions before anyone has asked one. And there is a second limit, the one Lord North found: the final move is not a division, it is a name, and only the narrowing part is arithmetic.

Curious what the same halving logic looks like when the field is fixed and public rather than anything at all? Try it against the world's countries in Where Are You Thinking Of?, or take on the broader set at the quizzes hub.

Frequently asked questions

Why does twenty questions use twenty and not some other number?

Because twenty yes-or-no answers can distinguish 1,048,576 possibilities, comfortably more than any field a person could actually be choosing from. Ten would reach only 1,024, too small to be interesting; thirty would reach over a billion, which is slack rather than useful. Twenty sits where the game is winnable but not easy.

How many things can twenty yes-or-no answers tell apart?

A little over a million, and only in ideal conditions. The exact figure is 2 to the power of 20, which is 1,048,576. That ceiling assumes every answer splits the remaining possibilities into two equal halves, and real questions almost never do, which is what keeps the game winnable for the person doing the thinking.

Who invented twenty questions?

Nobody known. The earliest clear description in the sources consulted for this piece is Hannah More's letter of 1786, describing a London dinner party at which she taught "the play of twenty questions" to Sir Joshua Reynolds and Lord Palmerston before beating Lord North with it. She treats the game as already established, with a name and a fixed limit, so it is older than her letter by an unknown margin. The 1946 American radio quiz of the same name popularised it; it did not originate it.

What is the best first question to ask?

The one whose answer you are least able to predict. A question that splits the possibilities evenly earns a full doubling of certainty, while a question you already know the answer to earns nothing. That is why broad categorical openers beat specific guesses: asking whether the thing is man-made comes far closer to the middle than asking whether it is a zebra, which rules out one thing.

Is it cheating to think of something very obscure?

No, and it is less effective than it feels. Obscurity does not make a field harder to cut in half, because asking whether the thing is man-made works the same on a lamp as on a lion. What obscurity defeats is the final step, where the questioner has to produce the actual name. Lord North lost in 1786 at the naming, not at the narrowing.

Sources

• William Roberts, Memoirs of the Life and Correspondence of Mrs. Hannah More, Vol. I, Harper & Brothers, New York, 1834, page 236, letter of 7 February 1786 - retrieved 10 August 2026, full scan at archive.org
• Cassell's Book of In-door Amusements, Card Games, and Fireside Fun, Cassell, Petter, Galpin & Co., London, 1881, "The Object Game" pages 35 to 36 and "Twenty Questions" page 49 - retrieved 10 August 2026, full scan at archive.org
• R. V. L. Hartley, Transmission of Information, Bell System Technical Journal, Vol. 7, July 1928, pages 535 to 563, measure defined at pages 540 to 541 - retrieved 10 August 2026, journal article at archive.org
• C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal, Vol. 27, pages 379 to 423 and 623 to 656, 1948, definition of the bit in the introduction - retrieved 10 August 2026, corrected reprint, Harvard mathematics
• Broadcasting, 4 February 1946, page 68, news item "Parlor Game Quiz" - retrieved 10 August 2026, issue scan at worldradiohistory.com