rocdocmac

Thanks for the Christmas tree idea! Changed the red to green. Hope my sketch is close enough! Don't know how to put an image into the spoiler section only - Sorry for that glitch.

Calculated.xlsx

Oooops, really slipped up here! Fifty seven appears to be the correct answer. Attached the updated solution with the two addtional arrangements added to the bottom row on the right. My sincere apology to all participants. Colored cube.xlsx

Replace the ? in each of these sequences with the correct value ... [1] 1 4 17 54 145 368 945 ? [2] 0 6 21 405 -504 ? [3] 2 15 10001 215441 ? [4] 7 8 5 3 9 8 1 6 3 ? [5] 15 52 99 144 175 180 147 ? [6] 0 5 8 8 2 3 5 2 9 4 ? [7] 1 2r πr² ⁴/₃ πr3 ? [8] 4/10 ?/102 168/103 1229/104 9592/105 78498/106 [9] 3 23 229 2869 43531 ? [10] 14 21 13 2 5 8 0 19 5 18 9 5 ? [11] 6 8 5 8 4 0 7 3 4 6 ? [12] 1 3 8 22 65 209 732 2780 ?

Colored cube.xlsx

If each side of a tetrahedron is an equilateral triangle painted white or black, five distinct color patterns are possible: (1) all sides white, (2) all black, (3) just one side white and the rest black, (4) just one side black and the rest white, and (5) two sides white, while the other two are black. If each side of a cube is painted red or blue or yellow, how many distinct color patterns are possible?

Did Stefan only glance at his friend's wall clock as he entered the house, but not when he left?