+1839 The number $N$ is a multiple of $7$. The base $2$ representation of $N$ is
10011010011ABC110_2.
Compute the ordered triple of digits $(A,B,C)$.
+1897 I didn't follow an algorithm. I legit tried every single possibilitility until I found 1.
When wee have A, B, C = 1, 0, 1, we get the number \(10011010011101110\)
Converting this into base 10, we have
\((10011010011101110)_2 = (1 × 2^{16}) + (0 × 2^{15}) + (0 × 2^{14}) + (1 × 2^{13}) + \\(1 × 2^{12}) + (0 × 2^{11}) + (1 × 2^{10}) + (0 × 2^9) + (0 × 2^8) + \\(1 × 2^7) + (1 × 2^6) + (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + \\(1 × 2^2) + (1 × 2^1) + (0 × 2^0) = (79086)_{10}\)
Dividing by 7, we get \(79086/7=11298\)
THUS,
The answer is \((A, B, C) = (1, 0, 1)\)
Thanks! :)
*I'm so tired
