2
Part of 2004 May Olympiad
Problems(2)
n packages of 3 candies to give away at birthday party
Source: X May Olympiad (Olimpiada de Mayo) 2004 L2 P2
9/19/2022
Pepito's mother wants to prepare packages of candies to give away at the birthday party, and for this she will buy assorted candies of different flavors. You can buy any number of candies but you can't choose how many of each taste. She wants to put one candy of each flavor in each package, and if this is not possible she will use only candy of one flavor and all the packages will have candies of that flavor. Determine the least number of candies that must be purchased in order to assemble the n packages. He explains why if he buys fewer candies, he is not sure that he will be able to assemble the packages the way he wants.
combinatorics
5 rectangles inside a 11x11 rectangle
Source: X May Olympiad (Olimpiada de Mayo) 2004 L1 P2
9/22/2022
Inside an square, Pablo drew a rectangle and extending its sides divided the square into rectangles, as shown in the figure.
https://cdn.artofproblemsolving.com/attachments/5/a/7774da7085f283b3aae74fb5ff472572571827.gif
Sofía did the same, but she also managed to make the lengths of the sides of the rectangles be whole numbers between and , all different. Show a figure like the one Sofia made.
geometryrectangle