Logic Puzzles · Billy-B
Logic Puzzle #33
From Billy-B's legendary 1001 Puzzle Collection — preserved on Puzz.com since 1998.
Puzzle #33
You have a box that fits inside of a box that fits inside of a box that fits inside of a box that fits inside of a box, for a total of 5 boxes. Assume that no two boxes can fit inside of a box, unless one is inside of the other (e.g. the two smallest boxes could not fit inside of the largest box, unless the smallest box was inside of the second smallest box), & the boxes cannot be altered (e.g. folded, cut, or torn). Using only these 5 boxes, how many different arrangements are there to place a gift in the boxes, if the gift can only be inside of the smallest box that is being used? Example: The gift in the second smallest box inside of the largest box would be 1 arrangement.
Reveal Answer
Let's number the boxes 1 through 5. The number of arrangements can be found by counting out all of the possible arrangements of the numbers 1, 2, 3, 4, & 5, but only for those numbers that are in ascending order (1, 2, 3, 4, 5, 12, 13, 14, 15, 23, 24, 25, 34, 35, etc.), for a total of 31 different arrangements.
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