1
Part of 2005 May Olympiad
Problems(2)
smallest 3-digit number wanted , product of two 2-digit numbers
Source: XI May Olympiad (Olimpiada de Mayo) 2005 L2 P1
9/19/2022
Find the smallest -digit number that is the product of two -digit numbers , so that the seven digits of these three numbers are all different.
number theoryDigits
6 geo figures and 6 colors
Source: XI May Olympiad (Olimpiada de Mayo) 2005 L1 P1
9/22/2022
On the blackboard were six figures: a circle, a triangle, a square, a trapezoid, a pentagon and a hexagon, painted in six colors: blue, white, red, yellow, green and brown. Each figure had only one color and all the figures were of different colors. The next day he wondered what color each figure was.
Paul replied: “The circle was red, the triangle was blue, the square was white, the trapezoid was green, the pentagon was brown, and the hexagon was yellow.
Sofía answered: “The circle was yellow, the triangle was green, the square was red, the trapezoid was blue, the pentagon was brown, and the hexagon was white.”
Pablo was wrong three times and Sofia twice, and it is known that the pentagon was brown.
Determine if it is possible to know with certainty what the color of each of the figures was.
combinatorics