MathDB

2

Part of 2007 May Olympiad

Problems(2)

checkers on n x n grid

Source: XIII May Olympiad (Olimpiada de Mayo) 2007 L2 P2

9/19/2022
Let n>2n>2 be an even integer. In the squares of a board of n×nn \times n, pieces must be placed so that in each column the number of chips is even and different from zero, and in each row the number of chips is odd. Determine the fewest number of checkers to place on the board to satisfy this rule. To show a configuration with that number of tokens and explain why with fewer tokens the rule.
combinatorics
51ab, a1b9 4-digit numbers wanted

Source: XIII May Olympiad (Olimpiada de Mayo) 2007 L1 P2

9/22/2022
Let X=a1b9X= a1b9 and Yab=51abY ab = 51ab be two positive integers where aa and bb are digits. XX is known to be multiple of a positive two-digit number nn and YY is the next multiple of that number nn. Find the number nn and the digits aa and bb. Justify why there are no other possibilities.
number theoryDigits