# Matthew Russell # Experimental Math # Homework 26 # I give permission to post this read `public_html/em12/hw24.txt`: read `public_html/em12/C26.txt`: ##################################################################################### # How many necklaces are there with 15 beads colored Red, # 23 beads colored Blue, and 12 beads colored Green? # The answer is 37564175809042384320. This can be found by: # CG:=Cn(15+23+12): # W:=WtCol(CG,3,x): # coeff(coeff(coeff(W,x[1],15),x[2],23),x[3],12); ##################################################################################### # In how many ways can you color the faces of a cube (up to rotational symmetry) # with 3 faces colored Red, 2 faces colored Blue, and one face colored Green? # The answer is 3. This can be found by: # S:={[4,2,1,6,5,3],[2,6,3,4,1,5],[1,4,2,5,3,6]}: # GP:=Gp(S): # W:=WtCol(GP,3,x): # coeff(coeff(coeff(W,x[1],3),x[2],2),x[3],1); #####################################################################################