The phrase to put two and two together means: to draw an inference (especially an obvious inference) from available evidence.
This phrase occurs, for example, in an interview of Ruth Chapman (born 1961), founder of the luxury fashion retailer Matches Fashion—interview by Sophie de Rosée, published in The Daily Telegraph (London, England) of Saturday 16th November 2013:
I found my first grey hairs in my late 20s and by the time I reached 40 I was colouring it every third week. My face started swelling up every three weeks, and I didn’t put two and two together until a mum at school told me it was the hair dye. I discovered that dark hair dye is really bad for you if used regularly. There are even links between dark hair dye and cancer.
The phrase to put two and two together dates back to the early 19th century, but the phrase two and two make four, used as a paradigm of the obvious conclusion, is first recorded in Miscellanies Upon Moral Subjects. The Second Part (London: Printed for Sam. Keeble and Jo. Hindmarsh, 1695), by Jeremy Collier (1650-1726), anti-theatrical polemicist and bishop of the nonjuring Church of England:
Luc. Are you sure your Idea of Matter is compleat?
Hyl. That the full Notion of Corporeity is comprized within the Three Dimensions, is as clear as that Two and Two makes Four.
The earliest occurrences of the phrase to put two and two together that I have found are as follows, in chronological order:
1-: From Facts and Evidences on the Subject of Baptism; in a Letter to a Deacon of a Baptist Church (London: Printed for C. Taylor by G. Hazard, 1815), by Charles Taylor (1756-1823):
How slightly do some very good people read their Bibles!—The Scripture is plain enough, to proper attention. Any who can put two and two together, to make four, may, and indeed must understand it.
2-: From Westminster Epilogue, published in The Hampshire Chronicle and Courier (Winchester, Hampshire, England) of Monday 10th February 1817—here, the phrase is punningly used in reference to pairs of dancers:
To your old comrades leave the vulgar job
Of training troops against a motley mob—
Be these your gentler arts, your easier path—
To visit all the world who visit Bath;
O’er balls and concerts to exert command,
To teach these where to sit, those where to stand;
As judge, to arbitrate is left to you,
Honour where honour, rank where rank is due;
To couple partners, no hard matter either,
’Tis only putting two and two together;
To settle all disputes,—as who’s to call,
Who’s to take place—to guide and govern all;
These be thy works, whate’er of some the scoff is,
No worthier officer or worthier office.
3, 4 & 5-: From articles about the divorce proceedings against Caroline of Brunswick (1768-1821), the estranged wife of George IV (1762-1830), King of the United Kingdom of Great Britain and Ireland from 1820 to 1830:
3-: From To the Lord Chancellor. On the Public Feeling with regard to the Proceedings against her Majesty, the Queen; and on the probable consequences of this struggle. London, July 12, 1820, by the English journalist and political reformer William Cobbett (1763-1835), published in Cobbett’s Weekly Political Register (London, England) of Saturday 15th July 1820:
I am no lawyer, and if it were possible, still less of a conjuror, but, being able to put two and two together, and to ascertain that they make four; being able to arrive at this conclusion, with mathematical certainty, I have applied my mathematics to the question just stated; and, twist them and turn them how I will; whether I add, subtract, multiply, or divide; whether I work by the rule of three, or by extraction of the square root; whether I proceed by vulgars * or by decimals, I am wholly unable to discover any reason for believing that the same reason which exists against having the Coronation now will not exist at any future period; unless, I say, her Majesty the Queen participate in the Coronation. And, I have no hesitation in expressing my opinion, as well as my hope, that it will never take place without such participation!
[…] My decided opinion is, that, when you and your colleagues have carefully put two and two together; and then put a one to the four, and by the total have multiplied twenty, the result will show you that it would be much better not to proceed with the trial any more than with the Coronation.
[* The term vulgar arithmetic was used to denote ordinary arithmetic, as opposed to decimal arithmetic.]
4-: From an account of the proceedings, published in The Morning Post (London, England) of Saturday 7th October 1820:
These things are so plain and palpable that whoever can put two and two together to make four, must understand them.
5-: From an account of the proceedings, published in The Cumberland Pacquet, and Ware’s Whitehaven Advertiser (Whitehaven, Cumberland, England) of Monday 6th November 1820:
Readers must put two and two together for themselves, instead of listening to every Radical deceiver.
6-: From A Grammar of the English Language, in which the Genius of the English Tongue is Consulted, and All Imitations of the Greek and Latin Grammars are Discarded; Adapted to the Comprehension of Persons Desirous of Teaching Themselves, and Intended for the Use of Schools and Young Persons in General (London: Printed and published by T. Dolby, ), by William Greatheed Lewis—in the following passage, the author denounces the fact that, while “professing to teach the principles of the English language”, “the majority of our grammars are little more than translations of the grammar of the Latin language”:
In the Roman language there are single words which will express the same idea that in our language requires several words; as “amabimur,” which in English is, “I shall be loved;” and grammarians, therefore, (although they always define a verb to be a word, &c.) call the words, “shall be loved” a passive verb, because the Latin word amabimur is so called. If, indeed, this be not the case, what, I ask then, could induce any man, capable of putting two and two together, to run into the monstrous absurdity of calling one word several, or several words one!