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| − | + | =Welcome to Shalom Keshet's= | |
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| − | + | =Mathematical Challenge of Christmas Cheer (MCCC)= | |
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| − | + | Merry Christmas ladies and gentlemen, today I have procured a set of Jolly Problems for you to solve, good luck! | |
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| − | + | ==Problem 1== | |
| − | + | Santa has brought 5 gifts for five people <math>A, B, C, D</math> and <math>E</math> and has placed them around the Christmas tree in a circular arrangement. If each of the gifts contains a surprise of one of the three types: toy, gadget and sweet, then the number of ways of distributing the surprises such that the gifts placed in adjacent positions get different surprise is ............ | |
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| − | \ | + | ==Problem 2== |
| − | + | Santa's elves have prepared a nutcracker festival and have arranged them as a triangle <math>\triangle ABC</math>. They want to know whether there is a line <math>\textit{\textrm{l}}</math> in the plane of <math>\triangle ABC</math> such that the intersection of the interior of <math>\triangle ABC</math> and the interior of its reflection <math>\triangle A'B'C'</math> in <math>\textit{\textrm{l}}</math> has an area more than <math>\frac{2}{3}</math> the area of <math>\triangle ABC</math>. | |
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Revision as of 14:47, 24 December 2024
Contents
Welcome to Shalom Keshet's
Mathematical Challenge of Christmas Cheer (MCCC)
Merry Christmas ladies and gentlemen, today I have procured a set of Jolly Problems for you to solve, good luck!
Problem 1
Santa has brought 5 gifts for five people 
and 
and has placed them around the Christmas tree in a circular arrangement. If each of the gifts contains a surprise of one of the three types: toy, gadget and sweet, then the number of ways of distributing the surprises such that the gifts placed in adjacent positions get different surprise is ............
Problem 2
Santa's elves have prepared a nutcracker festival and have arranged them as a triangle 
. They want to know whether there is a line 
in the plane of such that the intersection of the interior of and the interior of its reflection 
in has an area more than 
the area of .
