User:Shalomkeshet
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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 . Show the elves why such a line exists.
Problem 3
Little Timmy has been good this year and wishes for a mecharobot suit for Christmas. As his parents are associated with the Mafia, Santa has no choice but to comply with Timmy's wishes. The elves make a puzzle for Timmy to solve, and only if he solves it will he get his desired present.
The puzzle talks of a number 
, which is defined as the smallest positive integer such that this number multiplied by the peak gaming year, i.e., 
, is a perfect square and 
is a perfect cube. Timmy needs to find the remainder when is divided by 
.
Of course, you don't want to die either, so you need to help Timmy find the solution.
