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 $A, B, C, D$ and $E$ 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 $\triangle ABC$ . They want to know whether there is a line $\textit{\textrm{l}}$ in the plane of $\triangle ABC$ such that the intersection of the interior of $\triangle ABC$ and the interior of its reflection $\triangle A'B'C'$ in $\textit{\textrm{l}}$ has an area more than $\frac{2}{3}$ the area of $\triangle ABC$ .

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Contents

Welcome to Shalom Keshet's

Mathematical Challenge of Christmas Cheer (MCCC)

Problem 1

Problem 2