Can someone help me with these math problem?

The vertices of a cube are each labelled with one of the intergers 1,2,3,...8. a face-sum is the sum of the labels of he four vertices on a face of the cube. What is the maximum number of equal face-sums in any of these labelling A 5cm by 5cm by 4cm block is built from one hundred 1cm x 1cm x 1cm vubes, each of... show more The vertices of a cube are each labelled with one of the intergers 1,2,3,...8. a face-sum is the sum of the labels of he four vertices on a face of the cube. What is the maximum number of equal face-sums in any of these labelling

A 5cm by 5cm by 4cm block is built from one hundred 1cm x 1cm x 1cm vubes, each of which is coloured red or white. Te cubes are arranged in such way that no two cubes touch along a face are the same colour. What is the number of red faces in the interor of the block and why?

It is suprising fact that 1 x 2 x 3 x 4 x 5 x 6 = 8 x 9 x 10. It is even more suprising that 8 x 9 x10 x 11 x12 x 13 x 14 is equal to another such product of consecutive whole numbers. What is the smallest number in this other product and why?
Gina has three children and one of them is a teenager. When she multiplies their ages the result is 770. How old is the teenager and why?

How many different pairs of 2-digit numbers multiply to give a 3-digit number with all digits the same
Update: this is year 8 work....