I have made a box that I have allowed my players to find, it is the Mystical Box of locks, Mark 4. They were given one key to the box, let’s call this the red key. The Red key opens the red lock. pretty easy right? Inside they found the remaining three keys, for simplicity let’s call these the Orange, Yellow, and Green key. the magic of this item is when the Orange key is used it opens up the orange compartment, while if both Red and orange keys are used it opens a third compartment. my problem comes from this:

if I start back at the beginning with one key and one lock, it opens one compartment, while 2 keys give me 3 compartments (red, orange, and red/orange), 3 keys give me 7 compartments (R, O, Y, R/O, R/Y, O/Y, R/O/Y) and the 4 keys give me 15. every new tier I get double + 1 of the previous. so logically 5 keys should yield 31 compartments, but when I mapped it out I only came up with 30. at 6 keys I should have 63 compartments but only can figure out 60 combinations. the mythical box that I have hinted at has 7 keys. if the pattern follows what it should it would be 127 compartments but I have 121 mapped. did I F up somewhere or is there some formula that I am missing?

help me Inter-web Kenobi, you’re my only hope.

for anyone wondering the dimensions of the box are 24′ x 18′ x 12′ or 3 cubic feet, (I’m an idiot. but I’m not stupid :))