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…)

I was in a shop the other day and they were using a card terminal that wasn’t part of the till itself so they had to type in the amount I had bought.

And that lead me to think…

Has anybody ever bought something that is the value of their PIN?

For instance, if my PIN was 4253, and I bought something that was £42.53 then that would be a yes (remembering of course that when values are entered into tills and card units, it is always done by pence so that they would enter in 4253 and so would I).

(And, no, that isn’t my PIN, I’m not that stupid.  I did consider double-bluffing you too as that is the sort of thing I would do, but even I have a line that I daren’t cross on the Internet, and publising my PIN is about 250 yards away from that line!  As an aside, I used to, when I was with friends and getting money out of a cash machine, say four random digits as I entered my PIN just to confuse them.  Of course, me being me ended up confusing myself on a number of occasions resulting in me not putting the number in correctly. But I digress.)

Of course, there are some problems with this theory.  Depending if you’re rich or poor, or your PIN is a number in the low thousands or the high thousands.  One of my PINs is quite a high number, and I think I’m quite unlikely to come across this situation myself with that card, while the other was what started me thinking as the amount I bought was rather close to my PIN. If you’re rich, with a high number, say 9835 then £98.35 is nothing to you and you’re quite likely to spend that, yet with a low number PIN (say, 1378) then £13.78 is such a low amount that you would probably just hand over a twenty pound note.  On the other side, if you’re poor with a low number then £13.78 is, not a lot of money, but something you’d use a card for. £98.35 would probably be a weekly shop or something so something that would happen infrequently if at all.

I can honestly say that this has never happened to me. I just think these things up, honestly.  I don’t know why or where but they do show up in my mind.

I shall let you know if it ever does happen to me, and I’d be quite interested to hear if it has happened to you – though I’d advise against publishing the actual amounts and therefore also your PIN!

Except one person in the SABRE chat room this evening who told me that the show in question was called ‘The Incredible Games’.

It only ran for two series, and the computer in the first was David Walliams, who of course went on to do Little Britain.  It was a great show – why didn’t they do more!