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A door can be opened using a security code which consists of [#permalink]
21 Apr 2006, 01:14

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A door can be opened using a security code which consists of digits 1,2,3,4. You may press 1,2,3 or 4 buttons or all of them. If to open the door you must press 2 codes, in how many ways can you open the door?

Re: PS : Opening a door [#permalink]
21 Apr 2006, 10:06

This is a bit tricky.

If you mean to say that a security code consists of 4 digits, out of 1, 2, 3 and 4, and you need 2 such codes (ie, to press a total of 8 digits) to open the door, you're looking at 4^8 = 65536 codes, or ways to open the door. _________________

Re: PS : Opening a door [#permalink]
21 Apr 2006, 10:21

kapslock wrote:

This is a bit tricky.

If you mean to say that a security code consists of 4 digits, out of 1, 2, 3 and 4, and you need 2 such codes (ie, to press a total of 8 digits) to open the door, you're looking at 4^8 = 65536 codes, or ways to open the door.

I am confused too...

If we assume that we need 2 correct codes to open the door, then we have 4 choices each fo rthe other 2 codes. That gives 1*1*4*4 = 16 ways.... _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

The question is not clear... I'm assuming the code that one types in can have one, two, three or four digits.

Also, a number can be entered more than once In which case, the answer will be (4 + 16 + 64 + 256)^2 = big number.

Else, deowl's is the best answer. Order doesn't matter because you can enter any number, having a max. of 4 digits, and consisting only of 1, 2, 3, and 4.

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