MathDB

1

Part of 1997 May Olympiad

Problems(2)

no of 7-digit multiples of 388 that end in 388

Source: III May Olympiad (Olimpiada de Mayo) 1997 L2 P1

9/17/2022
How many seven-digit numbers are multiples of 388388 and end in 388388?
number theory
numbers 0-9 to 9 squares

Source: III May Olympiad (Olimpiada de Mayo) 1997 L1 P1

9/17/2022
On a square board with 99 squares (three by three), nine elements of the set S={0,1,2,3,4,5,6,7,8,9}S=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\} must be placed, different from each other, so that each one is in a box and the following conditions are met: ∙\bullet The sums of the numbers in the second and third rows are, respectively, double and triple the sum of the numbers in the first row. ∙\bullet The sum of the numbers in the second and third columns are, respectively, double and triple the sum of the numbers in the first column. Show all the possible ways to place elements of SS on the board, fulfilling the indicated conditions.
combinatorics