Problem 5. Milan and Aleksandar had a large box of chocolate candies, which they were to divide in the following way: First, Milan took 1 candy, and Aleksandar took two candies, then Milan took three, and Aleksandar took four candies, and so on, each taking one more candy alternately.

When the number of candies left in the box was less than the required number, the friend whose turn it was took all the remaining candies. How many candies were there in the box at the beginning, if Milan was the last to take candies and ended up with 101 candies.
Solution. Milan: $1+3+5+7+9+11+13+15+17+19=100$

Alexander: $2+4+6+8+10+12+14+16+18+20=110$

In the last taking, Milan took only one chocolate candy and had a total of 101. At the beginning, there were $101+110=211$ candies in the box.

## VI Department