Solution Step 0/0
A great craftsman created a beautiful chessboard for a king, who was so impressed he asked the craftsman to name his price. The craftsman said he wanted to be paid “only a few grains of rice,” in this manner: one grain of rice for the first square on the chessboard, two for the second square, four for the third, eight for the fourth, and so on, doubling the amount for each square up to the 64th square.
This did not sound like too much, so the king agreed.
Was this a good deal for the king?
This did not sound like too much, so the king agreed.
Was this a good deal for the king?
Explanations
It was not a good deal for the king. This problem illustrates the power of exponential growth.The first row or so of the chessboard would not cause any problems, but for the 21st square the king would have to pay over 1 million grains of rice, and for the 41st square, more than 1 trillion.
For the 64th square the king would owe the craftsman 2^63 and the same number minus 1 he would owe for all previous 63 squares combined. As a result thee king would owe the clever craftsman 2^64 minus 1, or 18,446,744,073,709,551,615, or 18+ quintillion grains of rice, or about 1,000 times the contemporary annual global rice harvest.
As it can be seen the deal is impossible to be fulfilled.
Check Good Deal
Check Bad but Doable
Check Manageable Deal
Check Disastrous Deal
