MathDB

It is known that the merchant’s

n

clients live in locations laid along the ring road. Of these,

k

customers have debts to the merchant for

a_1,a_2,...,a_k

rubles, and the merchant owes the remaining

n-k

clients, whose debts are

b_1,b_2,...,b_{n-k}

rubles, moreover,

a_1+a_2+...+a_k=b_1+b_2+...+b_{n-k}

. Prove that a merchant who has no money can pay all his debts and have paid all the customer debts, by starting a customer walk along the road from one of points and not missing any of their customers.

Problem Statement