PROBLEM STATEMENT
Cat Taro likes dice. He has a die which is a 1 x 1 x 1 cube where each face contains a number
between 1 and 6. Each number appears on exactly one face, and the sum of the numbers on opposite
faces is always 7.
There is an infinitely large board which is divided into 1 x 1 cells. The board has a coordinate
system in which the x-coordinate (the first coordinate) increases from left to right, while the
y-coordinate (the second coordinate) increases from bottom to top. Taro initially places the die
on the cell with coordinates (0, 0). The die shows '1' on the top face, '2' on the front face, and
'3' on the left face (so the bottom face shows '6', the back face shows '5', and the right face
shows '4').
Taro wants to move this die to cell (goalx, goaly) by performing a sequence of rotations. There
are two ways to rotate the die:
Rotate toward the right. This operation moves the die from cell (x, y) to cell (x+1, y).
Rotate toward the top. This operation moves the die from cell (x, y) to cell (x, y+1).
For example, if Taro's first rotation is toward the right, then the die will move to cell (1, 0)
and the top face will show '3'.
Return the number of sequences of rotations which move the die to cell (goalx, goaly), such that
the following conditions are satisfied:
The die must show '1' again on the top face when it reaches (goalx, goaly).
The die must not show '1' on the top face before it reaches (goalx, goaly).
DEFINITION
Class:DiceRotation
Method:theCount
Parameters:int, int
Returns:int
Method signature:int theCount(int goalx, int goaly)
NOTES
-The answer will always fit in a signed 32-bit integer.
CONSTRAINTS
-goalx will be between 1 and 1,000,000,000, inclusive.
-goaly will be between 1 and 1,000,000,000, inclusive.
EXAMPLES
0)
2
2
Returns: 2
There are two ways to move the die to cell (2,2) that satisfy the conditions:
right -> right -> up -> up
up -> up -> right -> right
1)
5
8
Returns: 2
2)
47
58
Returns: 2
3)
489
489
Returns: 2
4)
1000000000
1000000000
Returns: 2
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