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The obsolete British-English slang expression penny puzzle designated a sausage.

In this expression, the noun penny refers to inexpensiveness, and the noun puzzle to the mysterious nature of the ingredients—cf., below, quotation 2.

This expression was perhaps also chosen to designate a sausage in humorous allusion to penny puzzle in the sense of a puzzle-card sold on the street for one penny. The following, for example, is from the column Girls’ Gossip. By a Lady, published in the Evening Telegraph & Star and Sheffield Daily Times (Sheffield, Yorkshire, England) of Thursday 22^nd November 1888 [page 2, column 3]:

Penny Puzzles.

How many ways there are of turning what is styled an “honest penny!” Countless trifles are to be bought for this modest sum—some valueless in sense, whilst others, by their utility or as the means of entertainment, are essentially worth far more than the price paid. Just now penny puzzles seem to be the street hawker’s favourite ware. There is a large variety of these more or less ingeniously contrived to perplex the uninitiated and those not skilled in the mechanism of such things. Among the more popular puzzles is a card with two linked cords run through it, on which hang representative heads of the present and late Premiers severally. The puzzle is to get Lord Salisbury and Mr. Gladstone on one string, which it is announced is a means to solve the great Irish question.

These are, in chronological order, the earliest occurrences that I have found of the expression penny puzzle in the sense of a sausage:

1-: From A London Gamin’s Half-Crown’s Worth ¹, published in The Dundee Courier & Argus (Dundee, Angus, Scotland) of Wednesday 27^th December 1882 [page 4, column 2]:

“That precious cookshop seemed to haunt him. He bought a penny puzzle, as though to take the flavour of roast pork out of his mouth, and check the hankering for more of it.” “I beg pardon,” interrupted Mr Almonder, “what was it he bought?” “A penny puzzle—a saveloy, that is.”

¹ This story, by the British author and journalist James Greenwood (1832-1927), appeared under the title Three Half-Crowns, in Tag, Rag, & Co. Sketches of the People (London: Frederick Warne and Co., [1883]).

2-: From Passing English of the Victorian Era: A Dictionary of Heterodox English, Slang, and Phrase (London: George Routledge & Sons, Limited, [1909]), by the British author James Redding Ware (1832 – circa 1909) [page 194, column 2]:

Penny puzzle (Street, 1883). Sausage—because it is never found out. (See Bag o’ mystery.)

—Note: This is the definition of bag of mystery in James Redding Ware’s dictionary [page 15, column 2]:

Bags o’ Mystery. (Peoples’). A satirical term for sausages, because no man but the maker knows what is in them.
[…]
[…] The ‘bag’ refers to the gut which contained the chopped meat.

3-: From the column A Few Mair Daunders, published in the Leven Mail (Leven, Fife, Scotland) of Wednesday 22^nd January 1941 [page 3, column 4]:

Let me get back tae sausages. I’ve seen them made, but I’m no’ concerned wi’ their mak’-up. What I’m concerned aboot is that the wife wi’ a young family canna eke oot a meal withoot them, an’ tae tell the truth, bairns seem tae thrive on these penny puzzles.

4-: From the column A Few Mair Daunders, published in the Leven Mail (Leven, Fife, Scotland) of Wednesday 23^rd April 1941 [page 5, column 3]:

Let me get beck tae Lord Woolton. He says there’ll be a shortage o’ beef durin’ the next three months, but a mair plentifu’ supply o’ beef for makin’ sausages. He micht ha’e telt us what kind o’ beef it was that was unfit for sale unless it was mixed wi’ red ochre, biscuit meal, an’ spice, an’ then scoutin’ ² intae a skin. You’ve a’ heard o’ the landlady at a Fife fishin’ village. Her twa lodgers, gettin’ tired o’ fish, brocht in some link sausages, an’ asked her tae cook them for tea. “Hoo dae ye cook them?” she asked, an’ got the reply, “The same as herrin’.”
At tea time she cam’ in wi’ some burnt skins mutterin’—her, no’ the skins—Gosh, laddies, there’s no’ much o’ them left when ye tak’ the guts oot. Weel, freen’s, that has been my experience wi’ those penny puzzles, when they were fried the guts disappeared. A guid question for puzzle corner, what is a sausage, an’ give composition.

² Here, scouting means squirting.