This is about rice grains on a chessboard and…around Saturn! This is the third one in the series about problem solving.

Firstly, imagine placing one grain of rice in the first square, two in the second square, four in the third square, eight in the fourth square (as indicated in RED in the image below), and so on doubling the number with each new square.

chessboard
Source of this problem: T. Pappas’ book The Joy of Mathematics.

 

Of course, after a certain point, the square won’t be big enough to contain the rice grains that need to go on it and therefore it’s NOT possible to continue to do that all the way to the last square. But let’s imagine we could.

(If you have been reading my blogs–my personal blogs–this problem might have reminded you of another I published there, called Card Problem, Exponential Growth, and COVID19. For good reason too, because there are similarities between the two.)

Here’s the first question: How many grains of rice would be needed for the task?

Next, imagine lining up the rice grains from the above exercise on the equator of the planet Saturn horizontally, end-to-end, until they completely circled the planet. If more grains are available imagine adding another layer outside the first, and continuing to do so–building on the concentric circles of rice grains–until you run out of all the rice grains.

Saturn
Source of image of Saturn: https://www.cnet.com/news/hubble-delivers-knockout-view-of-saturn-in-the-summertime/. (If you follow the link, you’ll notice that the original image is much bigger. Obviously, what I have shared here is a cropped version of it!)

 

Here’s the second question: Would the ring of rice grains thus created around the planet extend as far out as the current ring around it? Why or why not?

Enjoy!

(Click here for the first one in the series, and here for the second one.)

 

 

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