Can someone help me with these math problem?

Question

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

this is year 8 work....

Answer 1

I've got correct answers for all five of the questions, but you said you wanted "help" with the problems, so I'll provide hints.
1 You don't even have to try any arrangement of numbers to know what the correct answer is.
2 how many blocks are in the interior? There's only one way , due to symmetry, that the blocks can be arranged such that no to touching faces are the same color.
3 which numbers in the second series are prime numbers?
4 a teenager is between what ages? the age of every kid is a whole number. when you multiply whole numbers you never get decimal places.
5. 111 is a multiple of ? all the three digit numbers are multiples of 111
If you want answers scroll down
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1 a cube has six faces. Every vertex is used by three faces. the sum of all the numbers 1 thru 18 is 36. multiply 36x3 (the number of times each number is used for all the faces in the cube). Divide by the 6 number of faces and you get 18. The vertexes can be numbered such that every face sum=18. One solution looking down at the cube and starting with the lower left corner and moving clockwise the top face 1,4,6,7 the bottom face 8,5,3,2
2 a 3-d checkerboard pattern is the only way to arrange the blocks. The interior is (5-2)x(5-2)x(4-2) blocks in size or 3x3x2 = 18 half are red = 9
3 8x9x10x11x12x13x14 both 11 and 13 are prime numbers in order to get the same product in a higher series of whole numbers whole number multiples of both prime numbers have to be in the product. first multiply the first series 8 x 9 x 10 x 11 x 12 x 13 x 14 = 17297280. the smallest possibility is 22 (2 x 11) thru 26 (2 x 13) then 26 thru 33 then 33 thru 39 and so on. Start dividing the numbers in sequence on a calculator into 17297280. you'll find that when you get to 65 thru 66 you're left with a whole number 4032. 67 won't work, but 65 will and then your left with 64.
4 just divide 770 by each number 13 thru 19 and you'll find that only 14 divides into 770 evenly. your left with 55 which is obviously divisible by 11 and 5
5 111 is a multiple of the prime number 37 you can easily find the prime factorization of all the three digit numbers keeping in mind that they are all multiples of 111.
111 = 3 x 37
222 = 2 x (3 x 37)
333 = 3 x (3 x 37)
444 = 4 x (3 x 37) = 2 x 2 x (3 x 37) gives you the first pair 12,37
555 = 5 x (3 x 37) 15,37
666 = 3 x 2 x (3 x 37) 18,37
21,37
24,37
27,37
6 pairs

Answer 2

6
half the cubes are red.

11 10 7

111 222 333 444 555 666 777 888 999 (to much work)

Answer 3

part one answer
as a member of a polically correct society I refuse to label any face.
part two answer
all the red blocks have red faces in the interior of the block because they were not painted white before being placed in the structure
Part three answer
the lowest number used in the other product would be the smallest number why simple logic
Part four answer
my guess would be the correct answer would be the one you are looking for

Answer 4

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?

14

Because that is the only number you can divide into 770 without getting a remainder

..Sorry I can't answer the rest. It's late and I'm tired

Answer 5

OH God...my head! Stooop! Owwieee. Why did I read this question about math..musta been morbid curiosity. Good luck..I'm sure you are so smart you really already have the answers and are just trying to torture us poor math challenged idiots. How mean! LOL..juss kidding. Love in Christ, ~J~ <><

Answer 6

hey baby... u shud do ur homework urself..... otherwise teacher will throw o\u outta the class.... ha ha ha ha...... Silly

Answer 7

was tat ure homework

Answer 8

I am going to do

Answer 9

hell for that homework
hell for the teacher
and hell for math

Answer 10

oh! boy this is which standard maths??