This most recent Sunday, I was reading Bill Gates’ The Road Ahead, and came across his discussing of obtaining all integer wattages between 0 W and 255 W by having 8 light bulbs (each with its own light switch) having wattage . I mentioned this problem to my class on Monday and was asked whether any integer between , for some , can be represented as the sum of distinct integers in the set . After a couple false proofs, I came up with one, and one of my students came up with a more elegant proof. The interested reader can find the proofs here. I have omitted the student’s name out of respect for his privacy.