Difference between revisions of "Invariant"
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== Problems == | == Problems == | ||
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| + | <math>\bullet</math> The positive integers <math>1</math> through <math>10</math> are written on a blackboard. At any given point, Evan can erase any three numbers <math>a</math>, <math>b</math>, and <math>c</math> and replace them with <math>\sqrt{a^{2}+b^{2}+c^{2}}</math>. What is the greatest number that can appear on the board at any given point? | ||
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| + | <math>\bullet</math> 2011 IMO Problem 2 (it is highly recommended that students watch the video solution, given the difficulty of the IMO) | ||
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{{stub}} | {{stub}} | ||
Latest revision as of 21:35, 23 July 2020
An invariant refers to a property of a situation that remains the same after multiple given operations.
Problems
The positive integers 
through 
are written on a blackboard. At any given point, Evan can erase any three numbers 
, 
, and 
and replace them with 
. What is the greatest number that can appear on the board at any given point?
2011 IMO Problem 2 (it is highly recommended that students watch the video solution, given the difficulty of the IMO)
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