During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

# Difference between revisions of "2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 6"

## Problem

There are $12$ stacks of $12$ coins. Each of the coins in $11$ of the $12$ stacks weighs $10$ grams each. Suppose the coins in the remaining stack each weigh $9.9$ 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.

## Solution

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 $\sum_{i=1}^{12}i=12\cdot {13}/2 = 78$ 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 $780-i\cdot(.1)$, the ith pile has the lighter coins.