The Manciple's Puzzle
This is another Dudeney Puzzle from The Canterbury Puzzles and until chasing it up I hadn't realised that it was actually Dudeney that invented this classic. I'll leave you to his poetic phrasing (although I will admit that the first paragraph is a struggle):
"The Manciple was an officer who had the care of buying victuals [goods and food] for an Inn of Court- like the Temple. The particular individual who accompanied the party was a wily man who had more than thirty masters and made fools of them all. Yet he was a man whom purchasers might take as an example how to be wise in buying of their victual.
It happened that at a certain stage of the journey the Miller and the Weaver sat down to a light repast. The Miller produced five loaves and the Weaver three. The Manciple coming upon the scene asked permission to eat with them, to which they agreed. When the Manciple had fed he laid down eight pieces of money and said with a sly smile, "settle betwixt yourselves how the money shall be fairly divided. 'Tis a riddle for thy wits."
A discussion followed, and many of the pilgrims joined in it. The Reve [I don't know what this word means and nor does Google] and the Sompnour [someone who summons you to court- obsolete] held that the Miller should receive five pieces and the Weaver three, the simple Ploughman was ridiculed for suggesting that the Miller should receive seven and the Weaver only one, while the Carpenter, the Monk, and the Cook insisted that the money should be divided equally between the two men."
"Various other opinions were urged with considerable vigour, until it was finally decided that the Manciple, as an expert in such matters, should himself settle the point. His decision was quite correct. What was it? Of course, all three are supposed to have eaten equal shares of the bread."
At first it may seem like the Reve and the Sompnour were correct because the Miller and the Weaver produced loaves in a ratio of 5 to 3 and so they should be rewarded in the same ratio.
However, that isn't the whole story. Although the Miller brought 5 loaves to the table xe [I'm not sure of gender] ate some of it xemself. What was left over from the 5 was passed over to the others. With that in mind the total actually given away was:
Which is in a ratio of 7 to 1, just like the lowly Ploughman suggested. I like this puzzle for the elegance of the numbers involved and the apparent simplicity of the situation leading to a hidden surprise: the original numbers just didn't smell of 7 or 1.