Money!

Logic Level 4

There are \( 108 \) points on a circle with the names \( A(0), A(1), \ldots , A(107) \). For future reference, let points \( A(n) \) and \( A(n+108) \) refer to the same point for any integer \(n\) .

Now Hugo enters the game with his big pockets filled with money. He places money with a positive integer value on each point, so that the sum of the value of the money placed on the points \( A(n), A(n+1), A(n+2), \dots , A(n+18), A(n+19) \) equals \( 1000 \) for every integer \( n \) with \( 0 \le n \le 107 \) .

Now by coincidence, the value of the money placed on the points \( A(1), A(19), A(50) \) equals \(1, 19, 50 \).

Can you compute now the value of the money Hugo placed on field \( A(100) \)? Type its value in the answer field.

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