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What I'm reading – "Problems To Sharpen The Young"

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Propositiones ad acuendos juvenes, "Problems to sharpen the young", is an early collection of recreational maths problems, generally attributed to Alcuin of York (roughly 735 – 804), although the authorship is not certain.

In it we find some familiar problems, such as the one about the man who has to transport a wolf, a goat, and a cabbage across a river. The wolf can't be left alone with the goat nor the goat with the cabbage.

"De lupo et capra etfasciculo cauli - A wolf, a goat and a bunch cabbages. A man had to take a wolf, a goat and a bunch of cabbages across a The only boat he could find could only take two of them at a time. he had been ordered to transfer all of these to the other side in condition. How could this be done."

After more than 1,000 years this puzzle remains seems to have retained its novelty and Googling "wolf, goat, cabbage" gets over a million hits.

Here's another I liked

De duobus hominibus boves ducentibus - Two men leading oxen. Two men were leading oxen along a road, and one said to the other: "Give me two oxen and I'll have as many as you have". Then the other said: "Now you give me two oxen and I'll have double the number you have." How many oxen were there, and how many did each have?"

The translations I'm reading are from Hadley and Singmaster [1] and a recent book by Marcel Danesi [2].

[1] Hadley, J. and Singmaster, D.  Problems to Sharpen the Young. The Mathematical Gazette , Mar., 1992, Vol. 76, No. 475.

[2] Danesi, Marcel. (2024) Alcuin's Recreational Mathematics: River Crossings and other Timeless Puzzles.

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