Question

put the numbers 1,2,3,4,5,6,7 and 8 at the vertices of a cuboid such that the sum of any three numbers on any face is not less than 10 .Find the minimum sum of the four numbers on a face

Answer 1

Answer:

minimum sum on one face is 16

Explanation:

condition : the sum of any three numbers on any face is not less than 10

1+2+3 = 6 < 10

1+3+4 = 8 < 10

1+3+5 = 9 < 10

1+4+5 = 10 = 10( should not be less than 10 = possible)

we have,

1+4+5+6 = 16. on one face and

2+3+7+9 = 21. on other face

Also,

1+4+5+7 = 17 on one face and

2+4+6+8 = 20 on other face

also,

1+4+5+8 = 18. on one face and

2+4+6+7 = 19. on the face

Answer 2

Answer:

The minimum sum of four numbers on a face is 14

Explanation:

A cuboid has six faces, as we all know.

Therefore, the following combinations of numbers from 1 to 8 on six different faces of a cuboid are generated under the requirement that the total of three numbers on each face is not less than 10:-

1. Front face - 3,4,7,8
2. Back face - 1,2,5,6
3. Left side face- 1,4,5,8
4. Right side face- 2,3,6,7
5. Upward face- 1,4,6,7
6. Downward face- 2,3,5,8

The sum of the first four digits of a face:-

1. Front face - 3+4+7+8 = 22
2. Back face - 1+2+5+6 = 14
3. Left side face- 1+4+5+8 = 18
4. Right side face- 2+3+6+7 = 18
5. Upward face- 1+4+6+7 = 18
6. Downward face- 2+3+5+8= 18

Hence, the minimum sum of four numbers on a face is 14.

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