Binary Combination Lock

if you have one of those combination padlocks with three tumblers, each with the digits 0-9 on them that means that there are a possible 1o*10*10 combinations of numbers that can be displayed.

10*10*10 = 1000 (obviously)

In order to have at least 1000 different combinations using tumblers that only have the digits 0-1 on them (the binary digits) you would have to have sufficient tumblers to display the number 999 (this is the same for the 3 tumblers using base 10, i.e. You can display 1000 numbers, all those up to 999 plus zero)

You display 999 in binary like this:

1111100111

So you would need 10 tumblers.

BUT the advantage is, with 10 tumblers using binary you can display a possible 1018 combinations. (1111111111 which is 1017, plus 0000000000 which is zero)

Ergo 10 tumblers displaying 0-1 is much more secure and therefore sensible. QED


Comments

Anonymous said…
I just had this idea. Great minds think alike.

Jerseyanarchist
NJ, USA
3:54 PM
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