3. Anya and Danya together weigh 82 kg, Danya and Tanya - 74 kg, Tanya and Vanya - 75 kg, Vanya and Manya - 65 kg, Manya and Anya - 62 kg. Who is the heaviest and how much does he/she weigh?
Answer. Vanya weighs 43 kg.

Solution. Adding the weights given in the condition: $82+74+75+65+62=358$, we get the doubled weight of all the children. That is, all the children together weigh $358 / 2=179$.

Anya, Danya, Tanya, and Vanya together weigh $82+75=157$, so Manya weighs 179 $157=22$.

Similarly, we find that Anya weighs 179-(74+65)=40, Danya weighs 179$(75+62)=42$, Tanya weighs $179-(82+65)=32$, and Vanya weighs $179-(74+62)=43$. Thus, the heaviest is Vanya, and he weighs 43 kg.