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## Lift buttons

Coming back from buying lunch across the street today, we entered the lift and proceeded to go through the routine of pressing the buttons for floors 5, 6, and 7, since we each needed to return to our desks briefly and we are spread across those floors of our office building. We lamented the fact that the process of floor selection was so incredibly inefficient, requiring us to hit three separate buttons to indicate what floors we needed the lift to stop at.

DMc pondered the idea of having 128 separate buttons, each one wired to tell the lift to stop at a different possible combination of the 7 floors in the building. For example, button 74 might tell the lift that people want to get off at floors 2, 4, and 7. All you need to do is calculate the value of 21+23+26 to get the correct button.

And then we realised we could make this incredibly cool idea even simpler to use, if we just renumbered the floors, so instead of having floors 1 through 7, we have floors 1, 2, 4, 8, 16, 32, and 64. So all you have to do is add up the numbers of the desired destination floors, and press the button with the number corresponding to the sum!