November’s Puzzle: Crazy Sequence

We posted a lengthy puzzle involving a long number at our Web site (InstantDoc ID 97007). Have you been able to determine the next number in that sequence? Let n be the zero-based position of the number in the sequence (0, 1, 2, 3, …). The actual number in the sequence is n factorials of n—that is, 0, 1!, 2!!, 3!!!, and so on. The lengthy last number in the sequence is 3!!!, so the next number in the sequence is 4!!!!. It would probably be prudent not to include the actual number in this space, as it wouldn’t leave space for anything else.

December’s Puzzle: Minimum Number of Weights

Can you determine the minimum number of weights required to measure any integer weight in the range 1 through 100 pounds using a scale? Also, can you generalize your answer for a range 1 through n pounds?