Most of us trust our mathematical instincts, at least a little bit. (If you have 100 apples and Billy takes 98, how many apples do you have left?) But there are famous cases where lack of mathematical intuition (or basic analysis) has led to erroneous conclusions. A classic story concerns the origins of the game of chess. A king announced to his kingdom that he was bored and wanted something new and clever to amuse him. The smartest person in the kingdom presented what we now know as the game of chess. The king played the game and was greatly amused. The king asked the inventor, "Tell me what I can give you from my kingdom as a reward." The inventor replied, "I do not ask for much, just place one grain of rice on the first square, two on the second, four on the third, until all 64 squares are filled." "It shall be so!" said the king, much to his regret, because he spent the rest of his days trying to grow enough rice to meet the promise (2^64 is a really large number).
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