The phrase to know how many beans make five, or to know how many beans it takes to make five, means to be sensible and intelligent.

The adjective blue, which sometimes precedes beans, is a meaningless fanciful intensive, as in the phrase once in a blue moon.

The following definition is from the review of How many beans make five? (The Individualist Bookshop, Ltd. – London, 1942), by Percival Lea Dewhurst Perry (1878-1956), published in the Larne Times (Larne, County Antrim, Ireland) of Thursday 23^rd July 1942:

In “How many beans make five?” the latest of the pungent Post-War Questions series of booklets Lord Perry points out that in our ordinary usage when we say of a man that he knows how many beans make five we mean that he is alert, commonsensical, adaptable and up to date, a man with all his buttons on, and with no screws loose.

The earliest instance of the phrase that I have found is from The Freeman’s Journal: or, The North-American Intelligencer (Philadelphia, Pennsylvania) of Wednesday 7^th January 1784—it can be assumed that the person using the phrase, “a gentleman from abroad”, is from Britain or Ireland:

A gentleman from abroad, who has lately purchased the rights of citizenship in this state, remarks that the Americans appear to be a very stubborn sett [sic] of people; the meanest mechanic amongst us not being willing to submit to our highest councils the decision of some of the plainest questions. For instance; he says he has found a cobler [sic] insisting strenuously that he knew how many blue beans make five as well as the council of censors, and that no vote could alter the matter. This spirit he alledges [sic], would not continue if we had but a sufficient standing army.

The second-earliest instance that I have found is from The Evening Packet, and Correspondent (Dublin, Ireland) of Thursday 7^th August 1828—I reproduce in its entirety this hard-hitting and well-written article:

LORD SHREWSBURY AND LORD ROSSMORE.

The correspondence between Lord Shrewsbury and Lord Rossmore is of a most amusing character. The naivetté [sic] with which the former takes for granted that the House of Peers “is subservient to any Minister,” proves his Lordship a wag of the first order, as it must be obvious to every man of sense, that such an opinion can have been only expressed with a view to take a rise (as the vulgar phrase is) out of the members of that august body. But the highest joke of all is, the grave assurance given to Lord Rossmore, that he would by his presence greatly enlighten the House of Commons, and almost single-handed carry the great question of Emancipation. Lord Shrewsbury seems to be fooling Lord Rossmore to the top of his bent¹.
We presume that the Noble Lords are intimately acquainted, and that, therefore, Lord Shrewsbury knows his man. We, upon this side of the Channel, who happen to be immediately acquainted with the history of the education, and other family misfortunes of Lord Rossmore, know that his Lordship, “with all his imperfections on his head,” would not have the imprudence, even in the fullness of his discontent, to venture upon the utterance of a single sentence, composed of six words of three syllables, in the presence of either of the Legislative Assemblies. If Lord Shrewsbury does not know Lord Rossmore otherwise than by the perusal of his public speeches, we can enlighten his Lordship, by informing him that those oratorical displays were written and reported for the Press by Mr. Lidwell, and so indifferently delivered by the Noble Speaker, that the Reporters of the London Press have lately resolved to take down and publish verbatim his Lordship’s future oratorical displays for the amusement of their readers. It is among the on dits of the day, that this resolve having been communicated to Lord Rossmore, induced his Lordship to determine quickly upon another resolve—namely, to withdraw himself altogether from public. His Lordship is not the indiscreet man that some people may esteem him, he knows well, right well, how many beans make five; he knows too the difference of responsibility attendant upon haranguing Henry Hunt² and Co., and the British House of Commons. His talents, such as they are, are of a stable nature, and though he has often been brought to the post, he is not to be prevailed on to cross the bar of the House of Commons.

¹ to fool somebody to the top of his/her bent: a phrase coined by the English poet and playwright William Shakespeare (1564-1616) in The Tragicall Historie of Hamlet, Prince of Denmarke (Quarto 2, 1604); here, the noun bent denotes the utmost degree of endurance; its literal sense is, in archery, the extent to which a bow may be bent.
² Henry Hunt (1773-1835) was a pioneer of working-class radicalism, whose eloquence earned him the nickname of Orator.

The phrase has given rise to humorous variations. For example, in The Odds Against Her, published in The Courier (Dundee, Scotland) of Monday 19^th January 1920, Concordia Merrel makes a character say:

“You can take it from me that Hamish Duan knows precisely how many cerulean beans make five.”

On Wednesday 5^th June 1935, The Tatler (London) published the review by Alan Bott of Hervey House, by the American actress and playwright Jane Cowl (1883-1950); Alan Bott wrote:

Round the corner in Brook Street, the duke is dallying behind closed curtains with one Sophy Gerould, who loves him dearly, knows how many political beans make five-and-a-half, and is well received in Society.

The following is from the review by Ivor Brown of a pantomime titled Jack and the Beanstalk, staged at Drury Lane—review published in The Illustrated London News (London) of Saturday 4^th January 1936:

Mr. Prince Littler, the promoter of this pantomime, certainly knows how many beans make five thousand, and has spread himself on a transformation scene which is a real bean-feast, imposing, yet reasonably brief.

The phrase has featured in several advertisements for Heinz Baked Beans; for example, this is from the Daily Herald (London) of Thursday 7^th August 1958:

YOU and HEINZ together: QUIZ No. 2

Q How many beans make five?

A At Heinz, sometimes the answer’s six, sometimes ten, sometimes twelve. It just depends how long it takes to find five absolutely perfect beans—and perfect, by Heinz standards, really means something. Every single bean goes through eight separate sorting processes!
Remember this next time you eat Heinz Baked Beans. It’s one of the reasons why they’re the very best beans you can buy. Heinz Baked Beans, 6d., 8d., 1/-, and the new family size 1/3d.

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