Henry Ernest Dudeney/Modern Puzzles/166 - Picture Presentation/Solution

by : $166$

 * Picture Presentation

Solution

 * $1023$, or $1024$ if you include the possibility of not giving any of his pictures at all.

Proof
For each picture, the collector can choose to give it away or to keep it.

He has to make this choice $10$ times in a row.

Hence he would have $2^{10} = 1024$ options, including not giving away any.