Today's puzzle

[sinjun]

Since I posted yesterday's earlier, here's the one on my calendar for today:

Find the number that best completes the sequence below.

1 4 16 ? 256

Comments

[flashfire.livejournal.com]

64. That's supposed to be a challenge? ;-)

All it is is the previous number multipled by 4. :-)

Re:

[wibbble]

Or it's increasing squares:

1^2 = 1
2^2 = 4
4^2 = 16
8^2 = 64
16^2 = 256

Perhaps a better puzzle would've been to find both explanations for the sequence. ;o)

Re:

[flashfire.livejournal.com]

That works, too. Looks like six of one, half a dozen of the other. You could still do 256 x 4 or 32² and come up with 1024.

Re:

[wibbble]

*nods*

If you double the root, because you're squaring, it's always going to be a four-fold increase.

I guessed 64 right away, and had to spend a minute thinking about /why/ it would be 64. There's just something about those powers of 2...

Re:

[flashfire.livejournal.com]

I still like the multiplier of 9 rule. No matter what number you take, no matter how large or small, you can multiply it by 9 and the total sum of all those numbers will always equal 9 once you've added them together.

To wit:

Key in a random number: 7,545,154,872,145 x 9 = 67,906,393,849,305. Add each of those numbers up and you get 72, and 7 + 2 = 9.

Of course, this was demonstrated in a simpler manner by just taking things like 5 x 9 = 45, and 4 + 5 = 9. ;-)

Re:

[wibbble]

That same rule works for multiples of three, too, except that it's either three or a multiple of three (ie, six or nine).