# Sissa ibn Dahir

Sissa ibn Dahir (also: Sessa) lived around approximately 300 after Christ. It applies according to for legends as the inventors chess - of the play.

When the game of chess was presented to the Indian ruler Shihram, it was so inspired that he let come Sissa ibn Dahir to itself and to him a desire freely placed. Sessa wished to fill nothing else as the 64 fields of the chessboard with Weizenkörnern, after the following method:

On the first field of the chessboard a grain, on the second field of two grains, on the third field of four grains, etc. up to 64. Field always the double number of the preceding field.

[itex] 1 + 2 + 4 + 8 +… = 2^0 + 2^1 + 2^2 + 2^3 +… + 2^ {63}< /math>

with

< math> \ sum_ {i=0} ^n 2^i = 2^ {n+1} - 1 [/itex] (Geometrical sum formula)

follows

< math> \ sum_ {i=0} ^ {63} 2^i = 2^ {64} - 1 = 18.446.744.073.709.551.615< /math>

Shihram instructed to let the bag wheat bring and inquired some days later whether the fool had taken his reward in receipt: But it had to hear that the computing masters had not computed the quantity of the Weizenkörner yet. After several days of continuous work the chief of the grain chamber announced that he could not apply 18 quintillion grain grains generally speaking realm.

In order to be able to transport such a quantity at all, one needs as many transporters that these - one behind the other set up - are enough 231,666 times around the earth. With an accepted weight of 0,1 gram per Weizenkorn the entire quantity would correspond to wheat on the chessboard for instance the 3000-fachen world-wide wheat harvest of the yearly 2004! (“The entire harvest quantity world-wide 2004 amounted to 624 millions t. “)

Now the question arose, how the promise could be redeemed. The computing master helped the ruler from the embarrassment, by recommending to him, it is Sissa ibn Dahir completely simply the grain grain for grain count to let.