The Mathemagician with the Power Cards

Chris, a mathemagician, has been performing a public show in a market. He has a pack of 5 cards, with 1, 2, 4, 8, and 16 dots on them, as illustrated below.

Image Courtesy: Computer Science Unplugged

Image Courtesy: Computer Science Unplugged

Now, Agnishom, one of the spectators, chooses a number between 1 and 31 (\(=1+2+4+8+16\)).

Will Chris always be able to select one or more of his cards such that their dots add up to Agnishom's number?

For example, if Agnishom chooses 5, Chris could pick these two cards shown below:

Image Courtesy: Computer Science Unplugged

Image Courtesy: Computer Science Unplugged

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