Y. Itoh's problem on random integral packings of the d-dimensional (4 × 4)-cube by (2 × 2)-cubes is formulated as follows: (2 × 2)-cubes come to the cube K_4 sequentially and randomly until it is possible in the following way: no (2 x 2)-cubes overlap, and all their centers are integer points in K_4. Further, all admissible positions at every step are equiprobable. This process continues until the packing becomes saturated. Find the mean number M of (2 × 2)-cubes in a random saturated packing of the (4 × 4)-cube. This paper provides the proof of the first nontrivial exponential bound of the mean number of cubes in a saturated packing in Itoh's problem: M ≥ (3/2)~d.
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机译：Y.关于由（2×2）多维数据集构成的d维（4×4）多维数据集的随机整体堆积的伊托问题的公式如下：（2×2）多维数据集依次随机地到达多维数据集K_4，直到可以通过以下方式实现：没有（2 x 2）立方体重叠，并且它们的所有中心都是K_4中的整数点。此外，每一步的所有允许位置都是等价的。这个过程一直持续到填充物饱和为止。在（4×4）多维数据集的随机饱和堆积中找到（2×2）多维数据集的均值M。本文证明了在伊藤问题中，M≥（3/2）〜d的饱和堆积中立方平均数的第一个非平凡指数界的证明。
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