Hnaflbaflsniflwhifltafl

Hnaflbaflsniflwhifltafl is a dwarfish game devised by the cunning inventor Morose Stronginthearm for Hugen, a previous Low King of the Dwarfs. Hugen had asked for a game that would teach young dwarfs the virtues of preparedness, strategy, boldness and quick thinking, and Morose came up with a board game that has some early resemblance to the Thud board.

The game swept through the dwarfish world, and was very popular. Hugen, being well pleased, asked Morose what he wanted as a reward. The inventor is on record as saying: "If it please you, your majesty, I ask for nothing more than that you should place one plk [a small gold piece then in general circulation] on the first square, two on the second, four on the third and so on until the board is filled." (This is a reference to the Roundworld legend of the Chinese sage who requested one piece of rice on the first, two on the second &c.)

The king agreed to this because, after all, it doesn't sound very much, and he had gold brought from the treasury. However, it soon became clear that what Morose had asked for was, in fact, all the gold in the universe.

'This,' as TP notes, 'presented a problem for the king, who had given his word, but he solved it by producing his axe and ordering two of his servants to drag Morose over to the window, where the light was better. At this point Morose hastily amended his request to "as much gold as he could carry", whereupon Hugen agreed and merely had one of his arms broken. "For," he said, "all should know that while Hnaflbaflsniflwhifltafl teaches preparedness, strategy, boldness and quick thinking, it is also important to know when not be too drhg'hgin clever by half."'

Lord Vetinari has a Hnaflbaflsniflwhifltafl board of great antiquity and value that Reacher Gilt congratulated him on. The slab was given to Vetinari by Low King Rhys Rhysson. Vetinari plays at a distance (via the clacks) with "an old friend from Uberwald," presumably Lady Margolotta.

It seems to be variously spelled, because Hnaflbaflwhiflsnifltafl is also recognised and used in the novels.

Answering the obvious question

If we base our answer on rice, not gold, it's still scary. If you number the squares of a chessboard from 0 to 63, the amount of rice on square n would then be 2^n. The amount of rice on the final square alone would therefore be 2^63 grains, which would require a very big chessboard.

The number of grains on #62 would be half that many, the number on #61 would be half again, and so on. If this series is continued to square #0, the sequence would add up to

N = 2^63 * sum ((1/2)^k, k=0, 63)

I won't prove it here but if |s| < 1, then

sum (s^k, k=0, ∞) = 1 / (1 - s)

It can also be shown that

sum (s^k, k=0, n)

= sum (s^k, k=0, ∞) - sum (s^k, k=n+1, ∞)

= sum (s^k, k=0, ∞) - s^(n+1) * sum (s^k, k=0, ∞)

= (1 - s^(n+1)) * sum (s^k, k=0, ∞)

= (1 - s^(n+1)) / (1 - s)

For our particular problem, s = 1/2 and n = 63. Therefore,

N = 2^63 * (1 - (1/2)^64) / (1 - 1/2)

which simplifies to

N = 2^64 - 1 grains.

If one grain of rice has a mass of only 20 mg, this would be a little short of 4 million million tonnes of rice (that's 4,000,000,000,000 tonnes!)!

"Not enough gold in the universe" doesn't cover it by any stretch. As of 2006, if you added all the gold ever mined on Roundworld together, the total weight would be 145,000 tonnes. Now, let's think about a gold coin. Even the purest on Roundworld are about 977 parts gold per 1000 parts - and how pure would a Discworldian coin be? Ankh-Morporkian coins we know have "all the gold content of seawater", but we can realistically expect a dwarfish gold coin to be pretty much what it says it is. Now a small gold piece would weigh perhaps 1/4 ounce. This equals 7.0875g, which is 354.375 times heavier than our grain of rice.

And that means 14,175,000,000,000,000 tonnes of gold!!

Which is 9,775,862,069 - nearly ten billion - times more gold than has ever been mined on Roundworld. He's lucky he only had an arm broken. The Chinese sage was executed by the time they'd reached the fifteenth square, for making the Emperor lose face for failing to honour his promise.

Annotation

The dwarfish name and the game itself resemble the Viking Tafl games, played on the somewhat less impressively-named Hnefatafl boards.