There is a story about a Chinese man who invented the game of Chess. The Chinese emperor at the time said something like ‘what can I give you for your reward?’. The gentleman replied that on his chessboard, he would have one piece of rice on one square, two on the next, four on the next, eight on the next, sixteen on the next and so forth.
I was told this story by my Granddad this afternoon, with the question ‘how many grains of rice were there in total?’. Being the former IT student that I am, I recognised this as being binary – which to a certain extent it is. A square on the chessboard is equivalent to 1 bit, a line on a chessboard is 8 squares, therefore a line is equivalent to a byte and would have 128 grains of rice on the line.
This is where things started to go a bit awry in my mind. Not having any pieces of paper to work things out on, and realising that it wasn’t simply a case of having 8×128 (the ninth square would be 256), I figured that this was impossible for me to work out. Nevertheless, I started to think that I might be able to work it out once I returned home and had the computer in front of me.
8×8 is 64, thought I, therefore a chessboard is effectively 64 bit, and the answer would be that number, multiplied by itself, minus 1 (which in binary would be 11111111111111111111111111111111111111111111111111111111111111111111111111)
Thinking that it would be easy to work out what the 64th number in the binary world would be, I did a quick Google search but gave up. (I have since worked this out, see below.)
That is when I started to write this blog post, thinking that I could allow you all to see me work through this mathematical problem. To give the story a proper retelling, I then searched Google for ‘rice chessboard’ or something like that. What should pop up high on the list, but an article from good old Wikipedia, which not only told me the story – the Chinese gentleman was in fact an ancient Indian mathmetitian named Sessa so -1 point for my grandfather there – but also the answer.
The answer is 18,446,744,073,709,551,615 – which when read out is eighteen million four hundred and forty six thousand seven hundred and forty four million seventy three million seven hundred and nine million five hundred and fifty one thousand six hundred and fifteen (I think anyway).
Now, having the answer to this conundrum has made me a much better person. Admittedly, I didn’t work it out myself (which actually would have made me a much better person) because I looked it up on the Internet. I was going to, but the Internet stopped me from doing it as it made it quite a pointless thing to do. The Internet has ruined my life. But it has made me a better person for it.
Possibly.
(To conclude, the 64th number in the ‘binary sequence’ is √(18446744073709551615 + 1) which is 4294967296. That bit was worked out by myself, so I wouldn’t be surprised if it’s wrong…)
