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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Latest revision as of 22:35, 23 July 2020

An invariant refers to a property of a situation that remains the same after multiple given operations.

Problems

$\bullet$ The positive integers $1$ through $10$ are written on a blackboard. At any given point, Evan can erase any three numbers $a$, $b$, and $c$ and replace them with $\sqrt{a^{2}+b^{2}+c^{2}}$. What is the greatest number that can appear on the board at any given point?

$\bullet$ 2011 IMO Problem 2 (it is highly recommended that students watch the video solution, given the difficulty of the IMO)


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