sum of numbers

[jls36278]

Ok...having trouble with this one...
Find the sum of all seven-digit numbers that can be written using only ones and zeros.

I'm guessing this can be done using exponents, however we have not gotten into this yet in class so I am having trouble. Only thing I'm coming up with is writing them all out and adding them up. Isn't there an easier way?

 

[Deleted member 4993]

Ok...having trouble with this one...
Find the sum of all seven-digit numbers that can be written using only ones and zeros.

I'm guessing this can be done using exponents, however we have not gotten into this yet in class so I am having trouble. Only thing I'm coming up with is writing them all out and adding them up. Isn't there an easier way?

I am guessing your quest is to:

Find the sum of all the seven digit numbers where the seven digit numbers are made with only 0 and 1.

If that is so - first find how many seven digit numbers can be made with 0 and 1.

 

[jls36278]

I'm guessing it's 49 because it would be 7x7???

 

[Deleted member 4993]

I'm guessing it's 49 because it would be 7x7???

No there are 64.

The unit digit can be filled in two ways (0 or 1) - 2

The ten digit can be filled in two ways (0 or 1) - 2 ? total = 2* 2 = 4

The hundred digit can be filled in two ways (0 or 1) - 2 ? total = 2* 2*2 = 8
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The million digit can be filled in two ways (0 or 1) - 2 ? 2*2*2*2*2*2 = 64


The ten-million digit can be filled in one way ( 1) - 2 ? 2*2*2*2*2*2*1 = 64