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January 7th, 2013, 02:40 PM  #1 
Newbie Joined: Dec 2012 Posts: 10 Thanks: 0  Possibilities with thirteen numbers
This is similar to one of my previous posts, but is quite different. There are 13 buttons (numbered 1, 2, 3, .....13)in this combination lock, and you have to figure out which ones can be pressed in. They can either be pushed in or left into their original extended position. You don't know how many buttons need to be pushed in (or left pushed out) to solve the lock (it could be none, 1, 3, 8, or all 13). How many possibile combinations are there? Any how do you arrive at that answer? Here's a photo of my lock. The buttons are in the front of the blanket chest and are springloaded. When you push one of the buttons, the corresponding lockpin on the top of the chest falls into place due to gravity. To let the lock return to the original position, you pull the lockpin upwards and the spring forces the button back out. After each attempt at pushing the buttons, the longer bar on top of the chest gets pushed down. If the combination is correct, you can push the bar all the way down. If incorrect, it only depressed part of the way. 
January 7th, 2013, 03:31 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,730 Thanks: 689  Re: Possibilities with thirteen numbers
Final answer 2^13. Expand (1+1)^13 binomial. The kth term is the number of ways that k buttons can be pushed.


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