Difference between revisions of "1980 Canadian MO Problems"
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==Problem 5== | ==Problem 5== | ||
| − | + | A parallelepiped has the property that all cross sections, which are parallel to any fixed face <math>F</math>, have the same perimeter as <math>F</math>. Determine whether or not any other poyhedron has this property. | |
[[1980 Canadian MO Problems/Problem 5 | Solution]] | [[1980 Canadian MO Problems/Problem 5 | Solution]] | ||
Revision as of 11:30, 2 March 2020
Problem 1
If 
is the decimal expansion of a number in base 
, such that it is divisible by 
, determine 
.
Problem 2
The numbers from 
to 
are printed on cards. The cards are shuffled and then laid out face up in 
rows of cards each. The cards in each row are rearranged to make them increase from left to right. The cards in each column are then rearranged to make them increase from top to bottom. In the final arrrangement, do the cards in the rows still increase from left to right?
Problem 3
A triangle is given with one constant angle and a constant inradius. Explicitly define all triangles for which the minimum perimeter is achieved.
Problem 4
A parallelepiped has the property that all cross sections, which are parallel to any fixed face 
, have the same perimeter as . Determine whether or not any other poyhedron has this property.
Problem 5
A parallelepiped has the property that all cross sections, which are parallel to any fixed face , have the same perimeter as . Determine whether or not any other poyhedron has this property.
