Thursday, May 22, 2008

Round 263

Date Released: May 22nd, 2008.
Date Rewarded: May 29th, 2008.

A Chomby was walking down a path one day when Jhudora appeared in front of it. "Solve this puzzle, and you may pass," she said.

What is the next number in this sequence?
1
721
727
5767
5791
5792
___

Please enter only a single number, with no other information. Otherwise, your entry will be disqualified.


Prize


Megachilli Hot Dog

Click to show/hide solution

First, you subtract the number to the previous number (assume that the number before the first one is 0). The sequence becomes:
1 721 727 5767 5791 5792 -> 1 720 6 5040 24 1.

We realize that 1 = 0! = 1!, 6 = 3!, 24 = 4!, 720 = 6!, 5040 = 7!, where ! is factorial [1].

Therefore, the original sequence can be decomposed at:
1 = 1! or (0!)
721 = 1! + 6!
727 = 1! + 6! + 3!
5767 = 1! + 6! + 3! + 7!
5791 = 1! + 6! + 3! + 7! + 4!
5792 = 1! + 6! + 3! + 7! + 4! + 1!
next number = 1! + 6! + 3! + 7! + 4! + 1! + n!

So, the sequence becomes:
1! (or 0!) 6! 3! 7! 4! 1! (or 0!) n!

Temporarily ignore the factorial sign and 'or 0!' part, we can rewrite the sequence as:
1 6 3 7 4 1 n

The sequence is the number of letters in each word of the first sentence of the puzzle.
"A Chomby was walking down a path one day..."

Therefore, n is 4. The next number should be: 1! + 6! + 3! + 7! + 4! + 1! + 4! = 5816.

Results: 1167 people guessed the correct answer earning themselves 1714 NP each.

References:
[1] Factorial

21 comments:

Tiffany said...

so, whats the answer?

Beth said...

It makes no sense

Tiffany said...

whats the answer whats the answer? is it 6 or 7?

AznDudeIsOn said...

Really... u guys thought it made no sense? This is fourth grade work. It's just a pattern, but with big numbers.

In summary of LC Solver's explanation, the pattern is 5 numbers long(meaning the pattern has 4 phases). On the last number which is shown in the question, it is the 6th number, and the 6th number is where the pattern starts again.

To find the answer, u gotta find phase 2 of the pattern, and apply it to the 6th number, to get the 7th number.


The answer is neither 6 or 7

AznDudeIsOn said...

hmm, i meant to say the pattern has 5 phases.

LC Solver said...

as azndudeison said. I hope you read the explanation. If you are confused about the explanation, you can comment here.

Megan said...

The answer is simple you must add 1! + 6!....... all the way to +n! And 0! and 1! bout equal 1 so 1+n=7 then n=6 so you add 1!.......6!(n!)

AznDudeIsOn said...

I wish I could quote or edit my post.

Anyways, when he says n is either 6 or 7, he means that n is either factorial 6! or factorial 7!.

Tiffany said...

kk gosh dont be so pushy

Marcella said...

I understook everything up to this

"Note that if we choose number 7 is the center, the numbers around it has a form:

3 + 4 = 7
6 + 1 = 7

So the number before last must be 1! We are not sure about the first number but we know:

1 (or 0) + n = 7

...could you possibly re-explain? I have no idea how you concluded that n is either 6 or 7. Even so, how do you figure out which it is?

Marcella said...

OH WOW I FEEL LIKE SUCH AND IDIOT! Still unable to understand what you wrote, I looked at the problem and saw it for myself. The last digit would be 6 or 7 because the first digit is 1 or 0!

Just wondering...is it a rule that the factorial of 0 is 1? Why is that? And would we really have to guess whether the first number is 1! or 0!?

Marcella said...

Do you think it would be safe to assume that the first number is 1!, since they used 1! later in the sequence instead of 0!?

Sorry for the multiple posts; I keep thinking as I wait and getting more excited :)

LC Solver said...

by definition, the factorial of 0 is 1. Check the reference for more information. I can't decide which is a good answer here either.

David said...

The good answer is 4.
How is it possible, you ask?
A Chomby was walking down a path.
1 6 3 7 4 1 ? if you count the letters.
Therefore the next factorial is 4. >.< I should've saw it sooner.

LC Solver said...

hey, great ideas David. Thanks for your brilliant comments.

un-bunny said...

you guys are brilliant

AznDudeIsOn said...

ohemgee, David... might be right, ugh, i already posted my answer too o_o.

jessicasjj07 said...

the answer is 5798 because 5798 - 5792 = 6 and the pattern goes 163741 so the next would be 6 making the answer 5798

mspink200 said...

You guys were all wrong haha.

LC Solver said...

Actually from David message, the answer is right. But we don't post the answer. Those who posted the answer is wrong.

No need to bash. We're here to learn and people made mistakes all the time.

gor8ers said...

1! = 1
1! + 6! = 721
1! + 6! + 3! = 727
1! + 6! + 3! + 7! = 5767
1! + 6! + 3! + 7! + 4! = 5791
1! + 6! + 3! + 7! + 4! + 1! = 5792

The pattern started repeating, the next number SHOULD have been 6! meaning we add 720 to 5792 and get what should have been the right answer, 6512.

The only thing that carries more weight than that theory is the stupidity of a trick pattern such as the factorials being the number of letters in each word of a sentence that appears weekly and should have no bearing on the puzzle.