Stacks of marbles

摘要

My nephew found a bag of identical marbles; it was labelled 250, but some were missing, If he laid out six of these to form an equilateral triangle, he could place one more in a "dimple" at the centre of the layer, and he noticed (as a little trigonometry would confirm), that the arrangement forms the corner of a cube, By adding further marbles to form whole layers below this, he could preserve the cube-corner arrangement until he had used all the marbles.