My Math Forum Possibilities with thirteen numbers

January 7th, 2013, 02:40 PM   #1
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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 spring-loaded. When you push one of the buttons, the corresponding lock-pin on the top of the chest falls into place due to gravity. To let the lock return to the original position, you pull the lock-pin 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.
Attached Images
 lock.jpg (77.2 KB, 178 views)

 January 7th, 2013, 03:31 PM #2 Global Moderator   Joined: May 2007 Posts: 6,805 Thanks: 716 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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