3
Part of 2007 May Olympiad
Problems(2)
8 children, all of different heights
Source: XIII May Olympiad (Olimpiada de Mayo) 2007 L2 P3
9/19/2022
Eight children, all of different heights, must form an orderly line from smallest to largest. We will say that the row has exactly one error if there is a child that is immediately behind another taller than it, and everyone else (except the first in line) is immediately behind a shorter one. of how many ways the eight children can line up with exactly one mistake?
combinatorics
6 positive integers one at each side of a cube
Source: XIII May Olympiad (Olimpiada de Mayo) 2007 L1 P3
9/22/2022
Jorge chooses different positive integers and writes one on each face of a cube. He threw his bucket three times.
The first time his cube showed the number facing up and also the sum of the numbers on the faces sides was . The second time his cube showed the number facing up and also the sum of the numbers on the faces sides was . The third time his cube showed the number up, plus all the numbers on the side faces. They turned out to be primes. What are the numbers that Jorge chose and how did he distribute them on the faces of the cube? Analyze all odds.Remember that is not prime.
number theory