I'm thinking of buying a gunsafe and need help confirming or disproving a manufacturers claim. They claim a safe with four buttons has 12,000,000 possible combinations. The rules for the safe are: 3 to 6 entries must be made. Each entry can be either 1,2,3 or 4 buttons. I would greatly appreciate assistance with this problem.
You can press one of four buttons individually in sequence or multiple buttons simultaneously(which would one entry so you would need four multi-button entries) or a combination of the two. Repetitions are allowed.
Examples: a-b-c-d or ab-bc-cd-da or abc-bcd-cda-dab or abcd-abc-ab-a etc.
P.S. I am a layman so please simplify the explanation if possible.