Brain Teasers
What's "Purrfect"?
"I'm 'purrfect'", purred Six, digging her claws into the top of the fence. "They call me Six because 6 is a 'purrfectly' perfect number."
"What's so perfect about it?" meowed the long-hair from the next yard.
"There's something special about 6 that makes it just perfect. Only a good thinker can figure it out!"
Six is right. 6 is called a perfect number. Figure out why. Then find the next greater perfect number!
"What's so perfect about it?" meowed the long-hair from the next yard.
"There's something special about 6 that makes it just perfect. Only a good thinker can figure it out!"
Six is right. 6 is called a perfect number. Figure out why. Then find the next greater perfect number!
Hint
Think about the factors of 6. See what happens when you add or multiply all of them (except for 6 itself) together.Answer
A perfect number is equal to the sum of all its whole number factors, except itself. So, 6 is a perfect number because the sum of its whole number factors, except itself, is 6 (1 + 2 + 3 = 6). The next greater perfect number is 28 because the sum of its whole number factors, except itself, 1, 2, 4, 7, and 14 add up to 28.Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
This was easy to me because last night I listened to a programme about Prime Numbers! Fun, aren't they?
I had to exercise the ole gray matter to get this one.
great one....... keep them coming
That was fun. I didn't get it. I thought it was because they could be multiplied to get 6.
Jan 27, 2006
this was interesting because it interpreted learning with my favorite animal . . . the kitty!
thats why i got the answer so fast!
thats why i got the answer so fast!
thats a cool one!! i got it after reading the hint .. i was thinkin of other things that could make it perfect!! good job!
Great one, although didb't get it right
I MEANT TO SAY DIDN'T.......geezz where is my brain....AND NO COMMENTS ABOUT THAT EITHER
reminded me of my high school days,where we studied perfect numbers,so instantly remebered the answer without any calculations
Much more a matter of definition and previous knowledge than calculation.
Actually, while you do need to have prior knowledge, there is some calculation involved. The formula for perfect numbers is:
2^(p-1)(2^p - 1)
where p and 2^p-1 are both prime.
2 is prime and 2^2-1=3 is prime, so 2^(2-1)(2^2-1) = 2*3 = 6.
These primes are called Mersenne primes and are involved in one strategy for find really large prime numbers.
The first 10 Mersenne primes are:
2, 3, 5, 7, 13, 17, 19, 31, 61, 89
The perfect numbers calculated from these grow much faster than the Mersenne primes. The 10th perfect number is:
2^(89-1) * (2^89 - 1) =
191,561,942,608,236,107,294,793,378, 084,303,638,130,997,321,548,169,216
2^(p-1)(2^p - 1)
where p and 2^p-1 are both prime.
2 is prime and 2^2-1=3 is prime, so 2^(2-1)(2^2-1) = 2*3 = 6.
These primes are called Mersenne primes and are involved in one strategy for find really large prime numbers.
The first 10 Mersenne primes are:
2, 3, 5, 7, 13, 17, 19, 31, 61, 89
The perfect numbers calculated from these grow much faster than the Mersenne primes. The 10th perfect number is:
2^(89-1) * (2^89 - 1) =
191,561,942,608,236,107,294,793,378, 084,303,638,130,997,321,548,169,216
For anyone interested, the scip model I used to solve this is available at:
https://tiny.cc/xk4j0y
(https://gist.github.com/saska-gist/
5bc77414aa77f44ea3db9007936dd933)
https://tiny.cc/xk4j0y
(https://gist.github.com/saska-gist/
5bc77414aa77f44ea3db9007936dd933)
To post a comment, please create an account and sign in.
Follow Braingle!