After much thought, I've hit upon a math puzzle that will work for my friend's little neighbor, the aspiring mathematician. Actually, I'm going to give her a two-part puzzle: a more straightforward version of the "littler math puzzle" posted below, and this little guy that I came up with yesterday while exploring the behavioral sciences building. Incidentally, why do "people scientists" and "medical scientists" always have such nicer buildings than "hard scientists?"
Anyway, here's the puzzle:
Most small numbers are pretty close to a prime number. For example, the number 22 isn't prime, but if I just change the second 2 into a 9, then it is (because 29 is prime). Similarly, 310 isn't prime, but 313 is. So it seems like often, all I have to do is change one digit in a number and I can make it into a prime number.
Unfortunately, that's not true for ALL numbers. There are some numbers that can't be made into a prime number just by changing one (and only one) digit. The question is, what is the smallest of these numbers?
Answer and explanation below the fold, as always.
Showing posts with label Puzzles. Show all posts
Showing posts with label Puzzles. Show all posts
Monday, August 30, 2010
A non-math puzzle
Here's a puzzle of a different sort:
It's been a while since I wrote one of these, but I think I'm getting better at it. It's still not up to NYT standards, but I'm making progress. And more importantly, I'm getting faster at it. The first crossword I ever wrote took me pretty much an entire summer. I finished this one in a week and a half, partly thanks to the fact that I'm now using some software to do the grid-setup and to keep track of the numbers and clues. Anyhow, here's the puzzle, have at it. I think it should be about equivalent to a hard Tuesday Times puzzle, but it may be a little harder than that.
In case you need it, or if you find a place I made a mistake, you can check the solution below the fold:
In case you need it, or if you find a place I made a mistake, you can check the solution below the fold:
∫ A littler math puzzle
I was still working on coming up with a puzzle for my friend's neighbor and I came up with this little guy, which I think is easier than the previous one, and also easier to explain. I haven't decided if I'm going to use it yet, but either way, it's a nice little puzzle so I wanted to share it with someone. Lucky you!
So here's the puzzle: Jill walks into her math classroom at the end of the school day to find Jack sitting sullenly at one of the desks. "What's the matter?" she asks.
"I'm gonna fail my math class," says Jack. "The teacher told me I could do this extra credit problem for him to get my grade up to a C-, but now I'll never be able to solve it and it's not my fault."
"What do you mean?" asks Jill, sympathetically.
"I mean, he told me to start with 1 and then start adding the odd numbers together in order on my calculator, you know, like 1+3+5+7 = 16, and so on. And then he said ' If you tell me what the first nine-digit number you can make just by adding together odd numbers in order is I'll round your grade up to a 70.0%.'"
"So what's the problem?" asks Jill, feeling annoyed that all she gets in this dialogue are questions.
"The problem is, I sat here for an hour adding together odd numbers on my calculator, but then I realized that my calculator can only display eight digits at a time anyway. So I'll never be able to figure it out!"
"Don't be silly!" said Jill, finally using a declarative. "I know what the first nine-digit number you can make by adding up consecutive odd numbers is."
And the question, of course, is "What is it?" Answer below the fold.
So here's the puzzle: Jill walks into her math classroom at the end of the school day to find Jack sitting sullenly at one of the desks. "What's the matter?" she asks.
"I'm gonna fail my math class," says Jack. "The teacher told me I could do this extra credit problem for him to get my grade up to a C-, but now I'll never be able to solve it and it's not my fault."
"What do you mean?" asks Jill, sympathetically.
"I mean, he told me to start with 1 and then start adding the odd numbers together in order on my calculator, you know, like 1+3+5+7 = 16, and so on. And then he said ' If you tell me what the first nine-digit number you can make just by adding together odd numbers in order is I'll round your grade up to a 70.0%.'"
"So what's the problem?" asks Jill, feeling annoyed that all she gets in this dialogue are questions.
"The problem is, I sat here for an hour adding together odd numbers on my calculator, but then I realized that my calculator can only display eight digits at a time anyway. So I'll never be able to figure it out!"
"Don't be silly!" said Jill, finally using a declarative. "I know what the first nine-digit number you can make by adding up consecutive odd numbers is."
And the question, of course, is "What is it?" Answer below the fold.
∫ A little math puzzle
A week or two ago an eighth grade girl who lived down the street from one of my good friends told me how much she liked math; I told her that I would send her a math puzzle and leave a little prize with my friend that she could claim if she solved it.
Actually, the first thing I told her was that she could have the prize if she figured out what perfect numbers were and described them to me. I figured she would consult an encyclopedia or her math teacher, but she proceeded to text "what is a perfect number" to ChaCha and read me the answer verbatim. So I called her a cheater and then resolved to come up with a puzzle she couldn't just look up the answer to.
Anyway, while I was walking to the grocery store the other day, the following little puzzle occurred to me. Unfortunately, I'm worried its a little too easy, since you can get the answer without really knowing what's going on, so it's not going to work as a puzzle form the little mathematician. But I liked it enough I wanted to put it someplace. Don't worry, its pretty easy, but it's based on something kind of neat that I didn't personally realize until the other day. Here goes:
The king's royal mathematician is about to retire, and he has to name a successor. He has two students, both with excellent marks on their exams and both of whom have shown real promise as mathematicians and as mental calculators. Thus, the old man announces a test: In the presence of the king and his court, he will write a 5-digit number on a piece of parchment and place the parchment on the table before the two students. Whichever one of them can be the first to correctly tell the king what the first (one's place) digit in the square of the number on the parchment is will be the new royal mathematician. However, to prevent them both from simply blurting out a guess (with a one-in-ten shot at winning), anyone who answers wrongly will be executed.
When the day of the test arrives the old man takes his quill pen, dips it in the bottle of ink, and carefully writes down his number of choice. Then, to ensure everything is fair, he squares the number himself, whispers the answer in the king's ear and turns around to place the parchment on the table and begin the test. However, just then the mathematician clutches at his chest, and falls over on the table, dead of a heart attack. As he falls, he knocks over the ink bottle, spilling it across the parchment and obscuring everything except the one's-place digit of the number he had written, which is a 7.
"Sire," says the first student, "I know the answer." He announces it to the court and the king nods in amazement.
The question is, what did he say, and, given that his life was on the line, how could he be so sure?
Answer and explanation is below the fold
Subscribe to:
Posts (Atom)