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

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

September 19, 2022
number theorymultiple

Problem Statement

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?
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