1. On January 1, 2013, a little boy was given a bag of chocolate candies, containing 300 candies. Each day, the little boy ate one candy. On Sundays, Karlson would fly over, and the little boy would treat him to a couple of candies. How many candies did Karlson eat? (January 1, 2013, was a Tuesday).

2. Petya can swap any two digits of different parity in the number 1974835. What is the largest number he can obtain this way?
1. Answer: 66.

Solution. In a full week, Little One eats 7 candies (one each day), and Karlson eats 2 (on Sunday), so together they eat 9 candies. Dividing 300 by 9 with a remainder, we get the quotient 33 and the remainder 3 (33$\cdot$9+3=300). In the last incomplete week, Little One will eat 3 candies: on Wednesday, Thursday, and Friday. Therefore, in 33 full weeks, Karlson will eat 33$\cdot$2=66 candies.

Grading criteria.

Correct answer without justification: 1 point.