Difference between revisions of "2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 6"
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== Solution== | == 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 <math>\sum_{i=1}^{12}i=12\cdot {13}/2 = 78</math> 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 <math>780-i\cdot(.1)</math>, the ith pile has the lighter coins. | |
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== See also == | == See also == |
Latest revision as of 03:18, 19 January 2019
Problem
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.
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 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.
See also
2017 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNM-PNM Problems and Solutions |