As for the dice, the sum of the number of spots of the surface and the opposite side is seven.
Taking into account this fact, how many ways to make a spot on the surface of the dice are there ?
As for the spots of 1, 4, and 5, it is same when you look at the dice from any direction, but as for the spots of 2, 3, and 6, it is different depending on the direction of the view.
Please consider this matter when you think ways.
Taking into account this fact, how many ways to make a spot on the surface of the dice are there ?
As for the spots of 1, 4, and 5, it is same when you look at the dice from any direction, but as for the spots of 2, 3, and 6, it is different depending on the direction of the view.
Please consider this matter when you think ways.
Answer
As for ways of the numbers' line of the side of the dice, there are two ways of direction of the line of two, three, four, five which are ways of clockwise and counter-clockwise.
In each case, since there are two ways of putting spots for two, three and six respectively, there are 2 × 2 × 2 = 8 ways of putting spots for two, three and six.
Therefore there are 8 × 2 = 16 ways in all.
16 ways
Solution
When I look at the spot of one on the surface of dice, the opposite side is six.
As for ways of the numbers' line of the side of the dice, there are two ways of direction of the line of two, three, four, five which are ways of clockwise and counter-clockwise.
In each case, since there are two ways of putting spots for two, three and six respectively, there are 2 × 2 × 2 = 8 ways of putting spots for two, three and six.
Therefore there are 8 × 2 = 16 ways in all.
