Rice Rice Baby

Did you ever hear the old Chinese story about the rice and the chessboard? The specifics are hazy, and I’m sure there are lots of variations anyway, but I remember the important details. Someone having performed some important task for the king asked that he be paid in rice. The king was to put one grain of rice on the first square of a chessboard, two on the next, four on the next and so on to fill the board with each square containing twice as much rice as the previous one. How much rice do you think this adds up to?

The answer is easy to calculate but difficult to imagine. There are 2N – 1 grains on the Nth square. 20 = 1 on the first, 21 = 2 on the second, 22 = 4 on the third, and so on. The last square, number 64, has , 263 = 9×1018 grains on it. That’s a nine followed by 18 zeros or nine billion billion. Let’s try to cut that down to something we can imagine.

There are about 2000 grains, give or take, in a reasonable portion of rice. If a person eats one portion every day she will eat 730,000 grains a year. That last square will feed her for about 1013 (ten thousand billion) years. I think we need to cut it down further.

There are six billion people alive right now. If they all loved rice as much as the example person in the previous paragraph and consumed it at the same rate of 730000 grains a year it would take about 2000 years to eat it all. The only problem is that none of us will live that long. We could eat it at twice the rate, say two portions a day each, but that will only reduce it to 1000 years. We need more people.

It’s estimated that there have been somewhere in the region of 100 billion people ever. Let’s assume that they all loved rice and would want to eat two portions a day for their entire lives. So we have 100 billion people each eating 1460000 grains of rice per year. How long would it last?

263 grains / (1011 people * 1460000 grains per person per year) = 63 years, a lot more than the average lifespan for most of human history. That single square of rice would comfortably feed two portions a day to every person who has ever lived for their entire life.

The rest of the board contains the same amount again (less one grain).