2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 6
There are stacks of coins. Each of the coins in of the stacks weighs grams each. Suppose the coins in the remaining stack each weigh grams. You are given one time access to a precise digital scale. Devise a plan to weigh some coins in precisely one weighing to determine which pile has the lighter coins.
On the digital scale, place one coin from the 1st pile, 2 from the 2nd, 3 from the 3rd, continuing in this fashion until you have placed 12 from the 12th pile. The scale will have coins. If the pile weighs 779.9g, the ﬁrst pile has the lighter coins. If the pile weighs 779.8g, the second pile has the lighter coins. And in general, if the pile weighs , the ith pile has the lighter coins.
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