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This 5-point problem was offered to third and fourth graders on one of the Math Kangaroo tests.

Out of 125 small, white and black cubes, the big cube was formed (see the picture). Every two adjacent cubes have different colors. The vertices of the big cube are black. How many white cubes does the big cube contain?

How many five digit numbers which use the digits 1, 2, 3, 4, and 5, with all different digits, have the following properties when looking at the number from left to right: the first two digits form a number divisible by 2, the first three digits from a number divisible by 3, the first four digits from a number divisible by 4, and the five digits number is divisible by 5?

Adam is drawing sets of 4 circles in such a way that in each set any 2 circles have exactly one point in common. In each set, he counts the number of points which lie on at least two circles. The greatest number of such points in a set is:

In a certain month there were 5 Saturdays and 5 Sundays, but only 4 Fridays and 4 Mondays. In the following month there will be
(A) 5 Wednesdays
(B) 5 Thursdays
(C) 5 Fridays
(D) 5 Saturdays
(E) 5 Sundays