The Answer to Dr. Foolish & Alice Liddell's Binary Puzzle

The binary value of Row #1 is: 32 + 4 = 36 (Only the 2nd & 5th squares are on)
The binary value of Row #2 is: 64 + 32 + 16 + 8 + 4 + 2 = 126 (Only the 7th square is off)
The binary value of Row #3 is: 32 + 8 + 4 = 44 (Only the 2nd, 4th & 5th squares are on)
The binary value of Row #4 is: 16 + 8 + 4 = 28 (Only the 3rd, 4th & 5th squares are on)
The binary value of Row #5 is: 8 (Only the 4th square is on)
The binary value of Row #6 is: 64 + 1 = 65 (Only the 1st & 7th squares are on)
The binary value of Row #7 is: 64 + 32 + 2 + 1 = 99 (Only the 3rd, 4th & 5th squares are off)

Again, here's the formula from the 2nd clue:

(64a + 32b + 16c + 8d + 4e + 2f + g) = Binary value of row.

Notice that each number in the formula by each variable is a power of 2; the power of 2 by the variable g is 1. (Yes, the number 1 counts because 2^0 = 1.)

Whenever a variable is multiplied by 1, it's the same as just the variable itself(whatever the value may be) because 1 is the number of multiplicative identity. But the only 2 numbers you were allowed to put in the variables are either 1(on) or 0(off) because that's how binary works.

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