The number N is a multiple of 7. The base 2 representation of N is 10110101010101ABC110.

Compute the ordered triple of digits (A,B,C).

Badada May 26, 2019

#1**+3 **

In place of ABC, you have 0s and 1s. Since they can occupy 3 spots, then you have the following possible placements:2^3 = 8 possible placements as follows:

000, 001, 010, 011, 100, 101, 110, 111. Using a short computer code to convert them, you get the following results:

B=2;a=(1,0,1,1,0,1,0,1,0,1,0,1,0,1**,0,1,0,**1,1,0 ); s=0;d=1;i=0; j=1; m=B^(count a-d)*a[0];s=s+m;cycle:m=B^(count a - (d+1))*a[i++];s=s+m;j++;d++; if(j

000 = 742726

001 = 742734

**010 = 742742 - Only this one is a multiple of 7**

011 = 742750

100 = 742758

101 = 742766

110 = 742774

111 = 742782

Guest May 26, 2019