Do you excel?

Logic is very important, and if you code or are a mathematician then sometimes you will not be surprised to find that even machines are defiant, recalcitrant and incorrigible, just like human beings. Take this very simple case, you have a two cylinder lock. In order to undo the lock you need a key which has cuts to match both cylinders (not being a locksmith I do not know the technical term for the cut, please enlighten me). So, if we call the cylinders A and B, then then we can say for any key C that if it is TRUE that the A cut matches the A cylinder AND it is TRUE the B cut matches the B cylinder that the key is a TRUE key that will open the lock.

Do you see? Both A and B must be TRUE to give us a TRUE key. If only A or only B matched you would say it is a FALSE key (it doesn’t fit). You would not be happy if only the A or the B cuts matched and it was still true that the key opened the lock. You might just as well have a single cylinder lock and wait for the intruder to walk in.

Well, we have many more cylinders in our locks these days to prevent that sort of picking and for four five, six or seven cylinder locks we expected the key to match every one for it to be a TRUE key. But in another context I found that for the equivalent of a four cylinder lock in Excel using AND() function that it gave me TRUE when only two of the four cylinders were TRUE. The other two were FALSE as you can see here….the correct answer is FALSE. This key should not be able to open the lock.

Ready and willing to be corrected, for I am sure that someone will spot the flaw (otherwise known as a falseness, which is not a village in Shetland) in this demonstration.