372

Part of 1957 Moscow Mathematical Olympiad

Problems(1)

MMO 372 Moscow MO 1957 divide a_i <= a_{i+1} <= 2a_i, into 2 groups

Source:

a_i \le a_{i+1} \le 2a_i

a_1 = 1, a_2,..., a_n

a_i \le a_{i+1} \le 2a_i

i = 1, 2, 3,..., n - 1

) and whose sum is even. Find whether it is possible to divide them into two groups so that the sum of numbers in one group is equal to the sum of numbers in the other group.

combinatoricsSumnumber theory