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According to an old Indian myth, Sissa ben Dahir was a courtier for
a king. Sissa worked very hard and invented a game which was played
on a board, similar to chess. The king decided to reward Sissa for
his dedication and asked what he would like. Sissa thought
carefully and then said, "I would like one grain of rice to be put
on the first square of my board, two on the second square, four on
the third square, eight on the fourth and so on." The king thought
this was a silly request, but little did he know ...

Below is a chess board with the first few squares filled with grains of rice as Sissa asked for:

Below is a chess board with the first few squares filled with grains of rice as Sissa asked for:

How many grains of rice would there be on the 8th square?

How many grains would you need altogether in order to fill up to the 15th square?

Estimate how many grains you would need in total to
fill the entire board in this way. Explain your thinking.

Perhaps Sissa was cleverer than the king thought!