2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 6

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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.

See also

2017 UNM-PNM Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10
All UNM-PNM Problems and Solutions
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