Tantalizer 478: Surprises
28 June 2017
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From New Scientist #1029, 2nd December 1976 [link]
King Ethelweed needed a new champion. So he commanded his three doughtiest knights to appear before him on the first Monday of the new year and bade them fight one another. They fought all day long until the eventide, when the king called a respite and awarded x ducats to the winner, y ducats to the second knight and z to the third. x, y and z are positive descending whole numbers.
To the valiant knights’ dismay, the same happened on the next and each following day, until King Ethelweed at length declared himself satisfied. One each day the same prizes of x, y and z were awarded, the being no ties on any day.
Thus it befell that Sir Kay gained the most ducats and became the king’s champion, even though he fared worse on the second day than on the first. Sir Lionel took home twenty ducats in all and Sir Morgan, despite winning top prize on the third day, amassed a mere nine.
Which was the final day and who won how many ducats on it?