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Part of 1998 May Olympiad

Problems(2)

4 digits from 1-9

Source: IV May Olympiad (Olimpiada de Mayo) 1998 L2 P1

Inés chose four different digits from the set

\{1,2,3,4,5,6,7,8,9\}

. He formed with them all possible four-digit numbers and added all those four-digit numbers. The result is

193314

. Find the four digits Inés chose.

number theoryDigits

3 colors for 6 rods

Source: IV May Olympiad (Olimpiada de Mayo) 1998 L1 P1

With six rods a piece like the one in the figure is constructed. The three outer rods are equal to each other. The three inner rods are equal to each other. You want to paint each rod a single color so that at each joining point, the three arriving rods have a different color. The rods can only be painted blue, white, red or green. In how many ways can the piece be painted? https://cdn.artofproblemsolving.com/attachments/1/1/91e6b388498613486477ab6b51735055e920cc.gif

combinatoricsColoring