## Two Weights?Math brain teasers require computations to solve.Martin rushed into the room bearing good news.
"Joseph, your idea worked! The company liked the idea of using only two types of weights to measure heavy objects!" announced Martin, giving the letter to Joseph. "I told you so. Given any two types of weights, you can measure objects that are above a certain weight," explained Joseph, reading the letter, "Well, as long as the two weights are not both even." Martin thought for a moment and then realized that he had no clue what Joseph meant by that, so he asked, "Huh? What? Isn't the new weight system designed to measure all types of objects?" Joseph smiled and replied, "Technically, yes. However, this system can't measure objects that weigh 1 pound, 2 pounds and other lighter objects. Besides, both weights are heavier than 10 pounds." "Really? But then why did the company like it?" wondered Martin, "What use does it have then? Can it measure 300 pounds? 90 pounds? 69 pounds?!" "Yes, yes, and no." Joseph laughed, "You're not getting the point. The company only weighs things 120 pounds or heavier. This weighing system can't measure 119 pounds but any object above 119 pounds can be expressed as a sum of combinations of these two weights." After hearing that, Martin was even more confused. Finally, Joseph said, "Look, 17 (5+5+7) can be expressed as a sum of only 5s and 7s. 18, on the other hand, can't. It works on the same principles. Think about it. You'll get it eventually." Assuming everything has integer weights, what were the two types of weights that Joseph suggested? ## What Next?
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