Name 9 of the Monuments of the Millennium, and for bonus name the category for the tenth.
Puzzle of the Month:
Puzzle: (source to be credited in January)
One of Mr. Jones, his wife, their son and Mr. Jones mother is an Engineer and another is a Doctor.
· If the Doctor is a male, then the Engineer is a male. · If the Engineer is younger than the Doctor, then the Engineer and the Doctor are not blood relatives. · If the Engineer is a female, then she and the Doctor are blood relatives.
Can you tell who is the Doctor and the Engineer?
November's Problem Solution:
The center pieces of each face are always in the same relationship to each other. Therefore, the number of ways the other pieces can be arranged in relation to them is:
Possible Arrangements of CP "Corner Pieces"
There are 8 Corner Pieces. Therefore, the possible different arrangements of them is 8! (ie 8x7x6x5x4x3x2x1) = 40320.
Each Corner Piece has three different orientations, so this must then be multiplied by 3 to the power 8 (ie 3x3x3x3x3x3x3x3) which equals 6561.
However, with the actual cube, once the second from last Corner Piece is placed, the last piece can have only one automatic orientation so this should be divided by 3 (effectively 3 to the power 7) which equals 2187.
Thus, total possible arrangements of Corner Pieces = 40320 x 2187 =88,179,840.
Possible Arrangements of EP "Edge Pieces"
There are 12 Edge Pieces. Therefore, the possible different arrangements of them is 12! (ie: 12x11x10x9x8x7x6x5x4x3x2x1) = 479,001,600. However, with the actual Cube (and unlike Corner Pieces) it is impossible to exchange just two Edge Pieces, so once the third from last is placed, the remaining two can have only one possible arrangement, so this total must be divided by 2, which equals 239,500,800.
Each Edge Piece has two different orientations, so this must then be multiplied by 2 to the power 12 (ie 2x2x2x2x2x2x2x2x2x2x2x2) which equals 6561. However, with the actual cube, once the third from last Edge Piece is placed, although the last two pieces will be in fixed positions, one can be reoriented but the last will always have a fixed orientation in relation to it. So this must be divided by 2 (effectively 2 to the power 11) which equals 2048.
Thus, total possible arrangements of Edge Pieces = 239,500,800 x 2048 =490,497,638,400.
Total possible arrangements = CP x EP
= 88,179,840 x 490,497,638,400 = 43,252,003,274,489,856,000
•
del.icio.us
digg
facebook
