Henry Ernest Dudeney/Modern Puzzles/98 - Curious Multiplication/Solution

by : $98$

 * Curious Multiplication

Solution
In the first column, write down the successive remainders on division by $2$:
 * $1 \, 0 \, 0 \, 0 \, 0 \, 1 \, 1$

which, when reversed, becomes:
 * $1 \, 1 \, 0 \, 0 \, 0 \, 0 \, 1$

This is $97$ in binary notation, or $2^0 + 2^5 + 2^6$.

In the second column, we take the numbers next to where the remainders are $1$, and get:
 * $23 \times 1 + 23 \times 2^5 + 23 \times 2^6$

which evaluates to $2231$.

Thus it is seen that the whole operation is being done in binary notation.