I'm looking forward to thinking about these puzzles Denise posted:
- 24 can be written as the sum of three square numbers. How?
- Can 24 be written as the sum of two consecutive integers? Can 24 be written as the sum of three or more consecutive integers? How many ways?
[Which reminds me: Did you figure out the consecutive-integer puzzle from MTaP #22?]
- How many ways can the letters M-A-T-H be arranged to form a 4-letter “word”? Okay, since there’s no 24 in the question, you’ve probably already guessed the answer — but can you prove it?
- 24 is the largest number divisible by all numbers less than its square root. Can you find all of the other numbers for which this is true?
- 24 is an abundant number, which means that if you add up all the numbers that divide evenly into 24 (except for 24 itself), the sum will be greater than 24 itself. How many other abundant numbers can you find which are less than 100?
- What is the ones digit in the number 24^24?
[That means 24 raised to the 24th power.]
I can't tell you my favorites, because I haven't had time to look through more than a few entries yet. (And if I don't post this link now, I might just forget.)
I think I'll savor it all on Sunday morning. Enjoy!