MathDB

1

Part of 2003 May Olympiad

Problems(2)

greatest possible no of 4-digit numbers, multiples of 36

Source: IX May Olympiad (Olimpiada de Mayo) 2003 L2 P1

9/19/2022
Four digits a,b,c,da, b, c, d, different from each other and different from zero, are chosen and the list of all the four-digit numbers that are obtained by exchanging the digits a,b,c,da, b, c, d is written. What digits must be chosen so that the list has the greatest possible number of four-digit numbers that are multiples of 3636?
number theorymultiple
abcd 4-digit wanted b=a+2, c=a+2, d=c+2

Source: IX May Olympiad (Olimpiada de Mayo) 2003 L1 P1

9/22/2022
Pedro writes all the numbers with four different digits that can be made with digits a,b,c,da, b, c, d, that meet the following conditions: a≠0 , b=a+2 , c=b+2 , d=c+2 a\ne 0 \, , \, b=a+2 \, , \, c=b+2 \, , \, d=c+2 Find the sum of all the numbers Pedro wrote.
number theoryDigitsalgebra