  Given a sequence $S=(s_1,\dots,s_m) \in [0, 1]^m$, a block $B$ of $S$ is a
subsequence $B=(s_i,s_{i+1},\dots,s_j)$. The size $b$ of a block $B$ is the sum
of its elements. It is proved in [1] that for each positive integer $n$, there
is a partition of $S$ into $n$ blocks $B_1, \dots , B_n$ with $|b_i - b_j| \le
1$ for every $i, j$. In this paper, we consider a generalization of the problem
in higher dimensions.
