[Guest]

Little Johnny was 13 years old and just moved to a new school. When he walked into class the teacher was teaching the students about prime numbers. She explained that a prime number is any number that is divisible ONLY by itself and 1. Johnny listened intently the whole class. For homework, the teacher asked the students to list out the first 10 prime numbers. For extra credit, she asked them to take the 5th and 7th prime numbers and multiply them together.

When Johnny got to school the next day, his teacher asked him the answer to the extra credit question.

"331" was Johnny's reply.

"That's impossible," she said. "What 2 prime numbers did you multiply together to get 331?"

Johnny answered, confidently, "12 and 23."

"Johnny, 12 isn't a prime number," his teacher explained.

Johnny then explained his answer and his teacher immediately gave him the extra credit. In fact, she told the whole class that little Johnny was a genius.

What did Johnny tell his teacher?

Edited December 26, 2008 by BeastMaster

[peace*out]

12 - 1+2=3, and 3 was prime?? im sorry - i have no idea...

[Guest]

Beacuse 12 is a unique number that can have prime factors?

12

^

2 6

^

2 3

[Guest]

Beacuse 12 is a unique number that can have prime factors?

12

^

2 6

^

2 3

Nope.

[Guest]

I think, that it has something to do with Johnny being 13.

[Guest]

Not sure how this relates, but notice that 12*23=/=331.

Probably something to do with the "together" thing... possibly he merged them.

[Guest]

Not sure how this relates, but notice that 12*23=/=331.

Probably something to do with the "together" thing... possibly he merged them.

He did not merge them, he multiplied them, but the discrepancy you've noted is part of his genius.

[Guest]

It is possible that he used a different base, I suppose, but I'm not in the mood to calculate the base it should be if it is a base. >_<

[unreality]

I calculated a possible base to ≈ 4.1816298, so lol I don't think that's it

[peace*out]

Little Johnny said sometinig that BM edited out??

BM did edit it...

Johnny said, "You're right", so the teacher told him he was a genius??

[Guest]

The teacher asked him to do the 5th and 7th prime number calculations.

Would 5 x 2 + 2 = 12

And 7 X 3 + 2 = 23 be in the right direction to solving it ?

Since 12 isn't a prime number, maybe it is a combination of numbers, or maybe 12 has a unique truth to it ?

[Guest]

Ok, so here's what I've put together so far. I don't know how any of it makes sense, but there are a lot of things about this riddle that apparently have more than meets the eye.

The 5th and 7th prime numbers are 11 and 17 (unless you count 1, then its 7 and 13) but either way its 187 or 91, nowhere near 331.

331 is a prime number itself so there's no way 2 numbers were directly multiplied together to get it.

I got nothing.

Haha, hope that helps someone

[Guest]

Ok, so here's what I've put together so far. I don't know how any of it makes sense, but there are a lot of things about this riddle that apparently have more than meets the eye.

The 5th and 7th prime numbers are 11 and 17 (unless you count 1, then its 7 and 13) but either way its 187 or 91, nowhere near 331.

331 is a prime number itself so there's no way 2 numbers were directly multiplied together to get it.

I got nothing.

Haha, hope that helps someone

Your 3rd spoiler made me burst out laughing at work hahaha

You're right, 331 has no multiples. 12 and 23 multiplied together - 276

Maybe 12 is a collective sum of other digits ? ,3,3,3,1,1,1 ?

So when she asked what numbers you multiplied, maybe Johnny didn't explain it fully. He could of multiplied 12 and 23 and then.....

Or maybe, ya, I got nothing either. I hope this question's answer isn't beyond common knowledge regarding math. I've been thinken about this for awhile now.

Here are all the prime numbers from 1-331 Maybe someone can see something

2 3 5 7 11 13 17 19 23 29

31 37 41 43 47 53 59 61 67 71

73 79 83 89 97 101 103 107 109 113

127 131 137 139 149 151 157 163 167 173

179 181 191 193 197 199 211 223 227 229

233 239 241 251 257 263 269 271 277 281

283 293 307 311 313 317 331

[Guest]

Little Johnny used Base 5 arithmetic.

12 = 7

23 = 13

331 = 91

[Guest]

Little Johnny used Base 5 arithmetic.

12 = 7

23 = 13

331 = 91

Twin Pop is correct - Good Job!!

I was really hoping it'd take longer than that. I was beginning to enjoy watching everyone virtually scratch their heads. Oh well, I guess I'll just have to make it harder next time.

[Guest]

Little Johnny used Base 5 arithmetic.

12 = 7

23 = 13

331 = 91

Can you please explain more,

meaning he removed multiples of 5 from each vaLue ? Why ?

[Guest]

Can you please explain more,

meaning he removed multiples of 5 from each vaLue ? Why ?

Our number system is Base 10, meaning that we count from 1 to 9 and then the next number is 1 ten and 0 ones. 11 is 1 ten and 1 one, and so on. 100 is ten times 10 or 1 hundred, 0 tens, and 0 ones. 142 in base 10 is 1 hundred, 4 tens, and 2 ones.

Base 5 system is where you count 1, 2, 3, 4 and then 10. 10 isn't really ten, it's 1 five and 0 ones. 11 is one five and 1 one, and so on. 100 is five times five or 1 twenty-five, 0 fives, and 0 ones. 142 in base 5 is 1 25, 4 fives, and 2 ones (or 47 in base 10).

So 12 in base 5 is really the number seven (1 five plus 2 ones). 23 in base 5 is really the number 13 (2 fives plus 3 ones). And 331 in base 5 is really the number ninety-one (3 twenty-fives plus 3 fives plus 1 one).

I hope that helps.

[Guest]

Our number system is Base 10, meaning that we count from 1 to 9 and then the next number is 1 ten and 0 ones. 11 is 1 ten and 1 one, and so on. 100 is ten times 10 or 1 hundred, 0 tens, and 0 ones. 142 in base 10 is 1 hundred, 4 tens, and 2 ones.

Base 5 system is where you count 1, 2, 3, 4 and then 10. 10 isn't really ten, it's 1 five and 0 ones. 11 is one five and 1 one, and so on. 100 is five times five or 1 twenty-five, 0 fives, and 0 ones. 142 in base 5 is 1 25, 4 fives, and 2 ones (or 47 in base 10).

So 12 in base 5 is really the number seven (1 five plus 2 ones). 23 in base 5 is really the number 13 (2 fives plus 3 ones). And 331 in base 5 is really the number ninety-one (3 twenty-fives plus 3 fives plus 1 one).

I hope that helps.

And all of this explains why Johnny's teacher called him a genius. He was only 13 years old, and he knew all of that. In fact, as kind of a personal inside joke for me, I intended for Johnny to really only be eight years old, but in base 5 you'd write that as 13.

In any event, good job TwinPop and good explaination. The only thing that was left out was to explain why we call it base "x". The base is named for how many distinct numerals are used to express numbers. In the case of base 10, you have ten different numerals, 0 through 9. In the case of base 5, you have five different numerals, 0 through 4. In base 2 (binary), you have two numerals, 0 and 1. In fact, you could use any symbolic placeholder you wanted (ie. hexadecimal uses 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F), but you just have to know what each symbol represents (obviously that gets more complicated) so it's just easier to use the numbers we have come to know and love. Well, now that I've thoroughly complicated the explaination...

For TwinPop, or anyone else somewhat familiar with bases, you'd be interested to know that this puzzle derived from a question that a friend of mine asked me. He wanted to know if a prime number in base 10 was still prime if you converted the number to a different base. The answer is YES, but you have to be careful. Let me explain...

In base 10, the number 7 is prime. When converted to base 5, this becomes 12 (1-five and 2-ones), which is also prime. However, you must do the conversion for the prime rule to be true. Watch...

In base 5, the number 12 is prime. If you don't convert this but just consider this "representation" of a number in base 10, you have twelve, which obviously isn't prime.

I could go on for days, but I won't.

Edited December 29, 2008 by BeastMaster

[Guest]

Hmmm hope this helps base five is just like computer language and 1 is 1 and 101 is 11.

Bascially the number jumps to ten after you reach that number and every number after that adds up to it, until you reach the base number.

[Guest]

Hmmm hope this helps base five is just like computer language and 1 is 1 and 101 is 11.

101 in base 5 or 2 is not equivalent to 11 in base 10.

In base 5, 101 is equivalent to 26 in base 10.

In base 2, 101 is equivalent to 5 in base 10.

What did you mean?

[Guest]

101 in base 5 or 2 is not equivalent to 11 in base 10.

In base 5, 101 is equivalent to 26 in base 10.

In base 2, 101 is equivalent to 5 in base 10.

What did you mean?

Sigh. Sorry i just keep making mistakes. Thanks for finding it.