Difference between revisions of "1969 IMO Problems/Problem 3"

 
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==Problem==
 
For each of <math>k = 1</math>, <math>2</math>, <math>3</math>, <math>4</math>, <math>5</math> find necessary and sufficient conditions on <math>a > 0</math> such that there
 
For each of <math>k = 1</math>, <math>2</math>, <math>3</math>, <math>4</math>, <math>5</math> find necessary and sufficient conditions on <math>a > 0</math> such that there
 
exists a tetrahedron with <math>k</math> edges length <math>a</math> and the remainder length <math>1</math>.
 
exists a tetrahedron with <math>k</math> edges length <math>a</math> and the remainder length <math>1</math>.
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==Solution==
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{{solution}}
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== See Also == {{IMO box|year=1969|num-b=2|num-a=4}}

Latest revision as of 13:37, 29 January 2021

Problem

For each of $k = 1$, $2$, $3$, $4$, $5$ find necessary and sufficient conditions on $a > 0$ such that there exists a tetrahedron with $k$ edges length $a$ and the remainder length $1$.

Solution

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See Also

1969 IMO (Problems) • Resources
Preceded by
Problem 2
1 2 3 4 5 6 Followed by
Problem 4
All IMO Problems and Solutions
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