One thousand million million, seven hundred million and nine million, and five hundred fifty-one thousand, and six hundred fifteen dirhams. This enormous sum is the result of the "Wheat and Chessboard" problem ($2^{64}-1$). The scribe has provided the final ten digits of the calculation: 18,446,744,073,709,551,615.
Some scholars have said that the doubling of the chessboard squares corresponds to the number of cubits of the Earth, and for the purpose of this verification, the board was made eight by eight squares.

CHAPTER

Abu Zayd al-Balkhi Abu Zayd al-Balkhi (850–934 AD) was a celebrated Persian polymath and geographer whose work often bridged the gap between science and philosophy. said: It has always been the custom of the wise to manifest the effects of their wisdom in everything they were capable of, by rendering obscure matters into examples and forms that fall under observation and the senses, so as to bring them closer to understanding. For the results of evidence and proofs are best understood when witnessed by the eye.

They often devised ways to establish things whose outward appearance would be entertainment original: "lahwan," meaning play or pastime. for the senses of the common folk, while their inward nature would be a discipline for the minds and senses of the elite, so that the fascination of the ignorant commoners would be the means for these things to spread among everyone, thus benefiting the whole.

In ancient or modern times, no two things have been found with such excellent structure and presence in play as chess and backgammon—except that one of them is forbidden and the other is permitted In traditional Islamic jurisprudence, backgammon (Nard) was often forbidden because it relies on dice (chance), while chess (Shatranj) was generally permitted as a game of skill and strategy.. For this reason, they have spread throughout all nations. The inventor of them claimed them as a point of pride over the clever devices of the Romans and the Persians. As for their inward meaning, he intended by them the two greatest matters over which creation has contended: the two schools of thought regarding Predestination and Compulsion, and Free Will and Necessity. The author is comparing the mechanics of the games to theology: backgammon represents "Fate" (the dice), while chess represents "Free Will" (the player's choice). One group said:

Regarding his phrase "cubits of the Earth," some scholars estimated a quarter of the Earth at twenty-seven hundred million and six hundred twelve thousand and eighty-two miles, and one hundred thirty-one miles and a fraction. If you multiply a quarter of the Earth by these miles and set the mile as one thousand nine hundred thirty-two cubits and a third and a half, the total cubits of a quarter of the Earth would be this sum. Then divide it by sixty-four, and the measure of a single square would be twenty-five million cubits and a hundred thousand and a fraction. Thus, what is close to one square is the cubits of a quarter of the Earth. And God knows best.