Est. 1998 — 27 years of woodworking knowledge
Puzzler -- PINs
Alex Y
A bank assigns 4-digit PINs to their customers' ATM cards. They use all the digits (including leading zeros). But fearing that some customers may be superstitious, they make it a practice never to have "13" appear in the PIN. I.e., "4153" is a legitimate PIN, but "4135" is not.
How many unique PINs can they assign using with this restriction in place?
Re: Puzzler -- PINs
Henry Higginbotham
One way to do this (in addition to a pencil and a bunch of sheets of paper), is to put all 10,000 numbers into a spreadsheet and have it search for "13" in "values." I did this and so have an answer, but I wonder if you're not looking for a more elegant way.
More Elegance, please ;-)
Re: Puzzler -- PINs
Ed in Leaside
There are few 'places' where 13 can appear ...
Re: More Elegance, please ;-)
Alex Y
True confession:
I found the more elegant solution to calculate the answer in my head.
And got it wrong.
TWICE!
Re: Puzzler -- PINs
Larry Barrett
and some of the places are in the same zip code as other places.
Re: Puzzler -- PINs
Ed in Leaside
So all the places except these places: 13xx, x13x, xx13.
Re: Puzzler -- PINs
Larry Barrett
So you would conclude that there are 10*10 + 10*10 + 10*10 = 300 of these places, except for double counting which means subtracting ...
Re: Puzzler -- PINs
Ed in Leaside
Do you mean this one? 1313
Re: Puzzler -- PINs
Larry Barrett
and that is the only double count.
So the answer (my answer and Ed's, I think) is the number of unique PINs that do not include the number 13 is 10000 - (300-1). Hope this is what Henry came up with.
Re: Puzzler -- PINs
Henry Higginbotham
Yes, same thing. Excel found 299 instances of "13," counting 1313 as only one instance. So 10,000 - 299 = 9701 assignable PINs.
I wanted to include a screen shot showing all 10,000 numbers, with the 13s highlighted, but I've just bought a new computer and don't yet have any program that can reduce the file size enough to post.
Re: Puzzler -- PINs
Alex Y
All of you got this one right. I need to be more careful with ones like this. :-)