In a fairy tale, the fairy grandmother has assured the queen that her yet unborn baby prince will not die until the following set of conditions is fulfilled.

A scroll shall be prepared, and on the day of the birth and every subsequent birthday, a letter of the Greek alphabet from Α to Ω inclusively, chosen at random with replacement, shall be entered on the scroll. On the day that all the 24 distinct letters from Α to Ω of the alphabet appears, the prince will die.

Determine the expectation of the prince's life in years.

The math/maths is (are?) impeccable, but do they take into account that the first letter is awarded at birth, not at the end of the first year, and that the prince (supposedly) will die on the day he gets that 24th letter?

(I think the answers hold, but am uncertain: the "fencepost problem" is ancient and common computer jargon for when a program does not properly handle the first or the last inputs in a set. as in "if there is a row of fenceposts 100 metres long, and they are spaced ten metres apart, how many fenceposts are there?")  Isn't the oriental custom to call the entire first year of life "age one"?  We might also wonder whether the quondam prediction also applies to princesses?

Posted by ed bottemiller on 2009-12-10 21:17:09