cobberone writes:
> While playing a game of Chess with my nephew the other nite, a thought
> occured to me . . .
Did you truly just come up with this question without having read it somewhere? This is a famous folktale. How famous? Well, not only have I read it quite a few times, but I own two children’s books retelling this story.
The version I’ve heard many times is not the one the OP posted. Are you thinking of the one Shag answered?
The version I remember has to do with a chessmaster and a chinese emperor who insisted in rewarding the chessmaster for something. After much back and forth, the chessmaster asked for grains of rice (following the 1 2 4 16 series). The emperor feels insulted that his generosity is wasted on such a stupid request, until they try to meet the request and realize that it would take all their crops forever. Instead, they gave him a job. A sucky deal for the chessmaster, if you ask me, but he didn’t want anything to begin with.
One bigass heap o’ sand, that’s what you’d have. Is there even that much sand on the planet?
Psst - see the part about there not being enough subatomic particles in the universe.
Yes, it’s not quite the same as the old folktale, but it’s pretty close. The folktale has grains of rice and it has the numbers only doubling each time. Still, it’s close enough that I wonder if cobberone actually came up with this idea himself.
Just doubling on every square is quite enough - 2[sup]64[/sup] - 1 is a heckuvalot of sand, wheat, rice or whatever.
My teacher set us a similar problem in class once involving payment for shoeing a horse - the smith suggested the King could pay him £1 for the first nail, £2 for the next, £3 for the next and so on, or 1d (old penny: 1/240 of a pound) for the first, 2d for the second, 4d for the third and so on. This was with four horseshoes and seven nails to the shoe. The numbers aren’t as astronomical but the King is still much worse off taking option 2 (which works out to £1,118,481 1s 3d).
Missed that. Thanks.
Here’s how far the number of grains of sand on the 64-th square goes beyond the number of grains of sand on Earth. I’ll take ultrafilter’s calculation that the number of grains is 10 ** (1.4 * (10 ** 19)). I don’t know how many subatomic particles there are in the universe, but let’s say that there are 10 ** 100 of them. (That’s a googol, 1 followed by 100 zeroes.) There aren’t enough subatomic particles in the universe to equal the number of grains of sand on the 64-th square.
Suppose that the entire universe is just a subatomic particle in a super-universe. Even if you take every subatomic particle in every universe in the super-universe, it wouldn’t be close to this number. Suppose that the super-universe is just a subatomic particle in a level-2-super-universe, and that every level-2-super-universe is just a subatomic particle in a level-3-super-universe, and so forth. You would have to include every subatomic particle in every universe in every level-2-super-universe in every level-3-super-universe . . . in every level-(10 ** 17)-super-universe to come anywhere close to the number of grains of sand on the 64-th square.