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PrintSouth African Mathematics Olympiad
South Africa algebra
Problem
Some balls were distributed into boxes which were arranged in a row as indicated below. Any four consecutive boxes always had a total of balls. How many balls were there in the th box?
Solution
If the number of balls in the boxes are denoted , then
Thus for all , which means that the numbers recur in cycles of length four. Since , it follows that .
Thus for all , which means that the numbers recur in cycles of length four. Since , it follows that .
Final answer
7
Techniques
Recurrence relations