Ok, finally I should finish this story.

You recall Bays’ theorem (sorry, I’m not going to bother writing it out) and use it to work out the probability that the base is B given that the largest digit is a 5. If you work this out (with some assumptions on prior probability distributions) I think that you get 6 as the most likely base. So you put 69 marbles in the bowl and pull the rope. Immediately Evil Eddie rushes into the room and slams you onto a platter, sticks an apple in your mouth and carries you off to your doom. As you pass Manvel’s chamber, you see him looking at you with pity. You notice that he has two hands with three fingers on each. Six fingers! But he didn’t use base six! You hear him say lamely “One hundered fifty three. I used base ten because I saw that you have ten fingers…” Oh well, that’s the way things go with probabilities…

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At least now I know.

I know that this was a pretty lame ending to the story, but that’s what I get for posting the first part of a story without having thought the rest out that well.