Page 28 - NUMINO Challenge_D1

Basic Concepts Magic Cube

Magic Cube is an arrangement in which numbers from 1 to 8
are written on each vertex of the cube without repetition,
such that the sums of the four numbers on each face are
equal.

Example Write numbers from 1 to 8 on each vertex 1
without repetition, so that the sums of the 4 2
numbers on each face are equal.

Class Notes

The sums of the numbers on two faces that are opposite each other are equal to the

sum of all numbers from 1 to 8. Therefore, the sum of the four numbers on one face is

36 2 .

There are eight cases in which the sum of the four numbers is .
(1, 2, 7, 8) (1, 3, 6, 8) (1, 4, 5, 8) (1, 4, , 7)

(2, 3, 5, 8) (2, 3, 6, ) (2, 4, 5, ) (3, 4, , )

The positions of numbers 1 and 2 are already given, therefore two arrangements of
numbers can be made according to the positions of 7 and 8.

1 1
2 2

In order to make the sum of one face 18 , the only two numbers that can be placed

under 1 and 7 are and . Write the numbers in the correct places,

where or is under . 1

1 1 1 1
2 2 2 2

25Number and Operations