Padlock combinations

[matt_london]

<PRE>I have a new padlock and I want to know how many different combinations there are for it. The padlock has 10 buttons, numbered 0-9. Each button can either be pressed down or raised (same as on or off). Currently you need to have 5 of the buttons pressed but someone trying to break it would not know that. Can anyone help?</PRE>

[chijiki]

The possible combinations are 10 for each button multiplied by 10 for each other button.
So, 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 gives you all the possibilities.

[Hammer]

Not quite, each button can be either up or down, so two choices each. The possible number of combinations is therefore 2x2x2x2x2x2x2x2x2x2 = 1024

[matt_london]

<PRE>Each button only has 2 combinations, either pressed down or raised. I've just had an idea that I think will work. Assume that the 10 buttons are binary numbers and see how many you can count up to, ie what is 1111111111 in binary. Answer: 1023 ?</PRE>

[mrbatfink]

and the last combination missing would be 0, hence 1023 and not 1024. if you can call not pushing or pulling any buttons a combination!