The Wheat and chessboard problem

1. How many grains of wheat must be given to the inventor in the 10th square?

2. How many grains of wheat must be given to the inventor only in the last square?

3. Make a graph showing the evolution of the amount of grains given in each square.

4. Calculate how many grains of wheat must be given, in total, to the inventor.

5. How may squares should have the chessboard to give 65535 grains of wheat to the inventor?

6. We have sacks of, give or take, 10000 grains of wheat.

   • How many sacks will we need to store the wheat?

   • If a sack full of wheat wheighs 30 kg, how many kg will all the sacks weigh?

7. Let's imagine the chessobard half as long and half as wide (4x4)

   • How many grains of wheat should the inventor receive at the last square?

   • How many grains of wheat should he receive if we triple the quantity of grains instead of doubling them in each new square?

   • And what if we multiply by 10 instead of doubling?

HOW THE STORY ENDS

They needed more than a week to calculate the amount of wheat they had to give to the inventor.

The king realized that it was impossible to pay the inventor, and he took revenge making him to count every single grain he was given, to be sure that the reward was the exact quantity of grains of wheat. 

• If the inventor was able to count 10 grains per second, how much time should he need to check that the king was giving him the exact amount of wheat?