Difference between revisions of "2015 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 4"
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== Solution== | == Solution== | ||
| − | + | Let the coins be called 1,2,3,4....11,12. | |
| − | + | Divide the coins into three groups of four, namely (1,2,3,4) (5,6,7,8) and (9,10,11,12) | |
| + | Then weigh any two groups, for instance (1,2,3,4) and (5,6,7,8). | ||
| + | Scenario 1: The two groups weighed are the same weight, that means the counterfeit coin is in the remaining group, namely (9,10,11,12). Now weigh three coins from the remaining group with three coins from the first group we weighed (1,2,3,4) and (5,6,7,8) For example we can weight (9,10,11) with (1,2,3). | ||
| + | Scenario 1.1: If the scale is balanced after weighing (9,10,11) and (1,2,3) then the counterfeit coin must be the remaining, unweighed coin, 12. | ||
| + | Scenario 1.2: If the scale is not balanced, label group (9,10,11,12) | ||
== See also == | == See also == | ||
Revision as of 06:21, 10 May 2022
Problem
There are 
coins in a parking meter and we know that one of them is counterfeit. The
counterfeit coin is either heavier or lighter than the others. How can we find the fake coin
and also if it is heavier or lighter in three weighings using a balance scale? Hint: 
.
Solution
Let the coins be called 1,2,3,4....11,12. Divide the coins into three groups of four, namely (1,2,3,4) (5,6,7,8) and (9,10,11,12) Then weigh any two groups, for instance (1,2,3,4) and (5,6,7,8). Scenario 1: The two groups weighed are the same weight, that means the counterfeit coin is in the remaining group, namely (9,10,11,12). Now weigh three coins from the remaining group with three coins from the first group we weighed (1,2,3,4) and (5,6,7,8) For example we can weight (9,10,11) with (1,2,3). Scenario 1.1: If the scale is balanced after weighing (9,10,11) and (1,2,3) then the counterfeit coin must be the remaining, unweighed coin, 12. Scenario 1.2: If the scale is not balanced, label group (9,10,11,12)
See also
| 2015 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNM-PNM Problems and Solutions | ||
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