Fig. 1 and Fig. 2 are development views of the cube in which the numbers from 1 to 6 were written to each face.
It is considered that the sum of numbers written to three faces gathering in the one vertex of each cube.
As for Fig.1, the greatest sum of numbers is 15.
In the case of Fig. 2, find the greatest sum of numbers.
It is considered that the sum of numbers written to three faces gathering in the one vertex of each cube.
As for Fig.1, the greatest sum of numbers is 15.
In the case of Fig. 2, find the greatest sum of numbers.
Answer
The face including the side BC is only a face of BCGF in addition to ABCD.
The next of B is F, since the next of C is G, it turns out that P is G and Q is F.
Since a face including the side BF is only a face of ABFE in addition to BCGF, it is found that R is A and S is E.
As a result of this work, as shown in Fig. 5, alphabet is assigned to all vertex.
Based on the alphabet number is put into the face, it will become as it is shown in Fig. 6.
In Fig. 6, the number with O is a number of the face which is not seen.
The greatest sum among a number of sums written in three faces gathering in one vertex according to this figure is 6 + 5 + 2 = 13.
13
Solution
As shown in Fig. 3, a sketch is drawn as a first step and alphabet A~H is assigned to each vertex.
Vertex of one face of the development view in the problem is given for ABCD, as shown in Fig. 4.
The face including the side BC is only a face of BCGF in addition to ABCD.
The next of B is F, since the next of C is G, it turns out that P is G and Q is F.
Since a face including the side BF is only a face of ABFE in addition to BCGF, it is found that R is A and S is E.
As a result of this work, as shown in Fig. 5, alphabet is assigned to all vertex.
Based on the alphabet number is put into the face, it will become as it is shown in Fig. 6.
In Fig. 6, the number with O is a number of the face which is not seen.
The greatest sum among a number of sums written in three faces gathering in one vertex according to this figure is 6 + 5 + 2 = 13.
