MathDB

Let

n

be an positive integer. Find the smallest integer

k

with the following property; Given any real numbers

a_1 , \cdots , a_d

such that

a_1 + a_2 + \cdots + a_d = n

and

0 \le a_i \le 1

for

i=1,2,\cdots ,d

, it is possible to partition these numbers into

k

groups (some of which may be empty) such that the sum of the numbers in each group is at most

1

Problem Statement