1. Mateja wrote down a hundred natural numbers one after another. She said about them: "The number at the fiftieth position is 50, and the number at the hundredth position is 100. If I add any three consecutive numbers, I get a sum of 2006." What is the number at the first position? What is the number at the ninety-ninth position?
III/1. Let's denote by $x$ the number that is in the 51st position. Then the number in the 52nd position is $1956-x$, since the sum $50+x+(1956-x)$ must equal 2006. The number in the 53rd position is again 50, the number in the 54th position is $x$, the number in the 55th position is $1956-x$..., the number in the 99th position is $x$, and the number in the 100th position is $1956-x$. Thus, $1956-x=100$, from which we calculate $x=1856$. Mateja wrote the numbers in a row as $100,50,1856,100,50,1856 \ldots, 50,1856,100$. The number in the first position is 100, and the number in the 99th position is 1856. [^0]