One, Two, Buckle My Shoe. I remember reading that Agatha Christie novel many years ago. Can't remember if the story is any good now.
Peckris' puzzle: You can make any number from 1-7 inclusive using the numbers 1, 2 and 4. Hence, 1, 2, 4 and 8 let you make any number from 1-15 inclusive.
1, 2, 4, 8, 16 can get you any number 1-31 inclusive.
1, 2, 4, 8,16, 32, 64, 128 and 256 get you any number 1-511 inclusive. That leaves you with 489 which is the number in the last envelope. There are probably a number of other solutions.