…and you have to guess what it is.

You were captured by a malevolent alien, who would really like to eat you for dinner. He told you his name, but since it is unpronounceable to humans, you like to call him Evil Eddie. Evil Eddie has a morbid sense of fairness and so, before roasting you with an apple stuck in your mouth and serving you with a side of glowing, purple, French-cut string beans, has locked you in a chamber carved out of the bedrock of a strange world. Before the polycarbide door slides shut with a hiss, Eddie tells you that you he is thinking of a number. If you can guess it, he will reluctantly release you. If not, well…let’s just hope that you can guess the number.

As you look around the cavern you see, in the dim and flickering light (does it come from torches? You don’t see any.), an enormous stone bowl, filled to the brim with glass marbles. How many are there? Thousands at least. Tens of thousands, perhaps. On the other side of the chamber is an identical bowl, but this one is empty. In the middle of the room, hanging from the ceiling is a rope. You hear Eddie’s voice thundering into the room “when you think that you know the number, put that many marbles in the empty bowl. Then pull the rope.”

Fortunately you have a friend. In an adjacent chamber is a benevolent alien. You don’t know his name, so you decide to call him Manvel. By some contrived plot device that the author has not taken the time to think of, you know that Manvel:

1) can read Evil Eddie’s mind (hence, knows the number),

2) is going to try to transmit this number to you, and

3) is going to do so by tapping out the digits (through the wall) in some base (could be base 10 (that’s what we normally use), could be base 2 (called binary. We think of computers as using base 2), could be any whole number base.

You listen and hear …tap… long pause …tap tap tap tap tap… long pause …tap tap tap… then silence.

You have the digits! They are 153. As stated above, you now know the number is:

You just don’t know what is. (I’ve glossed over the issue of big endian versus little endian order, but we are assuming, by aforementioned plot device, that big endian order has been used by Manvel).

So…how many marbles do you put in the bowl?

to be continued…

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I would put 69 in the bowl because I would assume that the largest number given would be one below the base, making this base 6. I can’t think of another reason to pick one base over another. Every number has at least one representation in a base between 2 and 10 such that one of the digits is one less than the base. (Base 2 will always give such a representation, but there is sometimes another one.) That would be a way to code both the base and the number just using the one set of taps. Of course, the alien could just choose to make the last tap the base and avoid the confusion altogether. Another problem with this argument is that 69 is already such a representation, and it has fewer digits, so I don’t know why he wouldn’t have chosen to represent it base 10. I look forward to seeing the answer.

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