A popular puzzle asks the solver to punctuate the following:
John where Willie had had had had had had had had had had had full marks.
The common answer is
John, where Willie had had “had,” had had “had had”; “had had” had had full marks.
But in 1955 a contributor to Eureka pointed out that a competing solver might have reversed the two phrases:
John, where Willie had had “had had,” had had “had”; “had had” had had full marks.
And in that case we might observe:
In the punctuation of the above, A, where B had had “… had had ‘had,’ had had ‘had had’; ‘had had’ had had …”, had had “… had had ‘had had,’ had had ‘had’; ‘had had’ had had …”; “had had had had had had had had had had had” had had two possible interpretations.
That observation itself can be punctuated in two different ways — a remark that might be communicated using an even longer string of hads. And so on forever — “there exist intelligible sentences containing (14 × 3n – 3) successive had‘s, where n is any non-negative integer.” “The solution of this recurrence relation is left as an exercise for the student.”
(“By Induction,” Eureka 18 [November 1955], 14. See Over and Out.)
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