i have a question for any maths wizz here. something from my real life.

 

i have a toolbox with a padlock that opens via a 4-digit sequence. so, for example 8734. and the padlock opens.

so when i lock the toolbox sometimes im a bit lazy and i just move the 4 slot around a bit, without touching the 873. one of the other guys reckons its easier for someone to work out the code to open the lock if i have only moved 1, instead of all 4 of them.

is he right? or does the law of averages mean there are still the same chances someone will guess it regardless of how many or few i move.

I think it's more a question of psychology than maths. If the would be 'breaker' is picking all 4 numbers at random each time then your strategy of just changing the last digit would be fine. But would a breaker work like that? When i've tried to break into these locks i usually change one number at a time - so your strategy would increase my chances of breaking in. No idea how common that tactic is though.

This reminds me a little of how best to play rock,paper, scissors: i particularly like the quote humans are predictably irrational.

 

thans for the reply prometheus. but i realised from your response that i didnt explain my question too good.

i get what you mean about the psychology of the guy trying to break the combination, totally makes sense.

but i was asking in a purely mathematical point of view.

On 07/11/2018 at 2:01 AM, Prometheus said:

If the would be 'breaker' is picking all 4 numbers at random each time then your strategy of just changing the last digit would be fine.

but i guess from this you think that a brain dead unthinking person, or a random machine,s chance are the same regardless of how the lock is arranged

14 minutes ago, jfoldbar said:

but i was asking in a purely mathematical point of view.

From a purely mathematical point of view, it makes no difference. Any number is just as probable as any other. It's like buying a lottery ticket: the number 1,2,3,4,5,67 are just as likely (unlikely) as any given 7 "random" numbers.

There are practical ways that just changing one of the digits could make a difference; for example if the person knew you had only changed one. Or if the others felt slightly stiffer (or were slightly shinier) because they were not used as much. Then they might realise that they only have to try 10 combinations and not all 10,000.

Details like this can be crucial to cryptanalysis. For example, the chips used for hardware encryption (eg in credit cards) have to draw exactly the same current for every operation; if there are any differences it can give clues to the way the hardware works, which can help crack the encryption.

thanks for replies guys.