Digital Logic Puzzle, "2 out of 10 voting" logic

I am tring to implement kind of "2 out of 10 voting" logic. This logic simply says if atleast 2 inputs out of given 10 inputs are "ON" then only output must be "ON".

So I have 10 digital inputs which needs to be mixed with logic gates OR, AND, NAND gates etc, Flip-flops RS, SR, Invertors..., so that above mentione开发者_StackOverflow中文版d logic works for 1 digital output.

One straight forward way of implementing this is to take 10C2 i.e 45 'AND' gate combinations, which will further clubbed in 1 'OR' gate to get desired output.

However I am just wondering for some tricky solution, Can anyone please suggest...

11 5 input OR gates, 5 2 input AND gates. Split your inputs as follows:

12345   67890
12340   67895
12390   67845
12890   67345
17890   62345

For each line, feed the left set of inputs into one OR gate, the right into another. AND those outputs together, and then take an OR of those 5 ANDs as your result.

The idea is to ensure, for any pair of inputs, one of the above lines always has one of them on the left and the other on the right.