## Number Series Brain Teaser

Barbara sent in this doozy. I have yet to figure it out.

What is the missing number?
6, 9, 27, 54, ?, 2241

Anyone have any ideas?

When you’re nearly comatose from over consumption of Thanksgiving’s finest, figure this out to give your brain some exercise.

1. Hmmm … 6 X 9 = 54, 27 X 2 = 54 … wait, do you know the answer, or have access to it? How will we know? Is it 83? ‘Cause 27 X 83 = 2241? That doesn’t seem to fit a pattern or make much sense, but hey, maybe worth a shot! 243? ‘Cause 9 X 27 = 243? …

Comment by DaveH on November 26, 2009 @ 1:23 pm
2. I think I’ve got it…(although to be honest, nothing clicked until I read one of the above posts).

6
9
27
54
X
2241

The pattern I found is that the sum of each two consecutive numbers is equal to the previous number squared (Although I only have proof of this for a few terms). For example:

9 + 27 = 6^2
27 + 54 = 9^2
54 + X = 27^2
X + 2241 = 54^2

1) 54 + X = 729
X = 675

2) X + 2241 = 2916
X = 675

I get the same value for X both times, which supports this hypothesis o_O

Comment by Parris on April 6, 2010 @ 2:58 am
3. 6 9 27 54 _ 2241

Ans:-675
6*6-9=27
9*9-27=54
27*27-54=675
54*54-675=2241

Comment by gandharav on January 19, 2011 @ 12:55 am
4. I think I have it, except for the 6, if you add the digits in each number they come to total of 9, eg 2 + 7 = 9, 5 + 4 = 9, 2+2+4+1 = 9, so missing number could be 81 or 621. What do you think?

Comment by ann johnston on July 28, 2011 @ 6:19 am
5. How about turning the 6 upside down!

Comment by ann johnston on July 28, 2011 @ 11:18 am