5.1. Mother gives pocket money to her children: 1 ruble to Anya, 2 rubles to Borya, 3 rubles to Vitya, then 4 rubles to Anya, 5 rubles to Borya and so on until she gives 202 rubles to Anya, and 203 rubles to Borya. By how many rubles will Anya receive more than Vitya?
# Answer: 68

Solution. Note that Anya will receive money one more time than Vitya. If we remove the first ruble, then each subsequent time Anya receives one more ruble than Vitya. Thus, it remains to determine how many such times there were. Apart from 1 ruble and 2 rubles, all the "moves" by mom break down into triples: $(203-2): 3=67$. Thus, on each round, Anya will receive one more ruble than Vitya, and with the very first move, she received an additional ruble. In total, the answer is 68.