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Googon's Garage Gadget


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#1 googon97

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Posted 26 February 2013 - 02:02 AM

If Googon has a normal garage opener with buttons 0-9 and enter and a code of 3 digits, it takes 3,000 button pushes to ensure the garage to open. Googon's Garage Gadget Guys builds a garage opener with 10 buttons. Googon realizes that there is no room for an enter button (he can't just take out a number 0-9). His garage opener opens if the code is pushed at any time. For example pushing 0123 could open the garage if the code is 012 or 123. Googon is worried that the garage opener is not safe. He needs your help on the issue (seriously he doesn't know the answer). How many times does someone need to push a button to ensure the garage will open? Can you prove that? Is their a pattern to the button pushing?


Edited by googon97, 26 February 2013 - 02:04 AM.

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#2 vistaptb

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Posted 26 February 2013 - 03:20 AM

Spoiler for The obvious answer would be


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#3 augustinus

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Posted 26 February 2013 - 11:44 AM

Spoiler for maybe they can

Edited by augustinus, 26 February 2013 - 11:54 AM.

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