### The Rizzoli Conundrum

I was in the Rizzoli book shop in Milan buying The Economist when I noticed that the wear pattern on the pinpad used to pay using a debit card was anything but uniform.  Unfortunately, I didn't have my phone with me so was unable to snap a picture, but it looked like this:

There was heavy wear on the buttons 1, 4, 7, 8, 9 and the green OK button. The buttons 2, 3, 5 and 6 showed little wear. What could cause this?

At first I assumed that Italian debit cards had four digit PINs and people might be able to choose their PIN and use a birth year. To check that I grabbed the latest statistics on the number of people living in Italy by age (statistics are available from ISTAT in CSV format) and wrote a small program to process that. Based on people aged 18 to 80, assuming 4 digit PINs equal to birth year the wear pattern would be: 9 (29.08%), 1 (27.46%), 7 (7.39%), 6 (7.34%), 5 (6.39%), 8 (6.19%), 4 (6.13%), 3 (4.84%), 2 (2.70%), 0 (2.47%) (which isn't terribly surprising as there would have had to be a sudden drop in the birth rate in 1950s and 1960s Italy for the observed pattern).

Then I asked some Italians about their debit card PINs. Italian PINs are 5 digits long (not 4) and are chosen by the bank and cannot be changed.

So, can anyone come up with an explanation of what I observed?

PS If anyone's in Milan and can walk into Rizzoli and snap a picture of the pinpad (at the till straight in the front door) it would be cool.

Dave O said…
Only things I can think of:

1) Some variation of Benford's Law is at play
2) The buttons were not all from the same batch during manufacturing. For example, maybe 1, 4, 7, 8, and 9 were made in a separate batch of differing quality, resulting in greater-than-usual wear than the numbers in the other batch.
3) The PIN is a hash value of some kind, and the hash function results in an unusually large distribution for the worn digits. Example: Geographic region of the customer might be encoded in the PIN, and perhaps a small number of regions are more popular than others.
4) If the screen's dialog uses digits to navigate the menus, perhaps those worn numbers reflect the most commonly selected menu items.
5) Similar to #3: If the bank is using common words as the basis for generating digits, then the resulting number sequences may reflect higher frequencies for common letters.
6) All the buttons were worn down evenly, but only some of the digits were recently replaced with new buttons. Or, someone smashed the buttons, and only the broken ones were recently replaced.
Confusion said…
I'm going with your option 6. ATM's attract a lot of vandalism.
Unknown said…
Another option is if 1, 4, 7, 8, 9 and OK tend to get pressed with the index finger, at least if you’re right-handed, and it causes more wear than the middle or ring fingers on 2, 3, 5 and 6.
Vinny Burgoo said…
Or people station their index fingers above the top right button, perhaps because that seems the best way of shielding the pad from prying eyes, and prod the numbers from there. Vertical and near-vertical prodding might produce slightly less wear than prodding at an angle.

Or something else entirely.
Alex said…
Or the Italians never fixed this little beauty?

http://www.theregister.co.uk/2005/10/21/phantoms_and_rogues/
sesqu said…
Was there a window nearby? Maybe the wear pattern was simply the summer sun hitting some keys.

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